There’s a Downing Street in Manhattan. #10 is a park with a statue of Winston Churchill. It’s fulla weeds and crap.
Only a portion of the White House is set aside as the President’s residence. The majority is used for the actual operation of the Executive Branch of the government. 10 Downing Street, on the other hand, is just a place for the PM to live. Of course it isn’t as big!
One point to consider in this discussion is that there is some symbolism at play here, in both the U.S. and the U.K.
Under the U.S. doctrine of separation of powers, it’s symbolically significant that there’s a big building associated with the Executive Branch, to counter-balance the big building associated with the Legislative Brance.
Under a parliamentary system, there’s different symbolism. The House of Commons is where it’s at, for both the Legislature and the Executive: the Executive sits in the Commons and stays in power there only so long as they control a majority in the Legislature. So the Parliament buildings are the symbol of both branches of government.
Not surprisingly, Canada follows the British pattern: the official residence of our Prime Minister (which we’ve only had for about ~60 years), is 24 Sussex Drive. It’s not particularly accessible (except to the occasional nighttime intruder, but our crack teams of Inuit soapstone carvers provide the necessary security
), and is screened from public view by trees. There are no public tours, and I doubt that the average Canadian could pick it our of a photo array. Consciously or not, our symbolism of government is Parliament. Similarly at the provincial level, as far as I know, none of the provinces even have official residences for the Premiers, just housing allowances.
The only residences that tend to be big and impressive are the official residences of the Governor General and the Lieutenant Governors, who are our equivalent of the head of state when the Queen isn’t around. Rideau Hall in Ottawa is not far from 24 Sussex, and it’s everything 24 Sussex isn’t - big and impressive, open to the public, used for public events like the swearing in of governments, investitures to the Order of Canada, etc. The residences of the Lieutenant Governors, traditionally called “Government House”, play a similar role at the provincial level, even if the Lieutenant Governor no longer actually lives there.
Who lives next door? Do they share walls?
Well, the South African Embassy is just across the street from Rideau House in Ottawa, at the intersection of Sussex and a little street originally called “Rideau Gate” - until the Ottawa City Council renamed Rideau Gate in the mid-80s as part of the anti-apartheid movement. So for a while, the Embassy’s mailing address was:
Embassy of the Republic of South Africa
1, Nelson Mandela Road
Ottawa, Ontario

(I see from Googling it that they’re now giving the mailing address as 15 Sussex Drive.)
It’s worth noting that the symbolism of 10 Downing Street is fairly recent. And I suspect strongly related to television. It’s far easier to show a picture of the closed door as visual shorthand for “this is what the PM thinks/said/will do”, than to fully explain the context of any one statement.
It should also be noted that until direct bomb attacks against the government in the early 80s, anybody could wander down Downing Street as a normal road.
Nope. Most of the building is taken up with offices and other official rooms. The PM will spend much of their average day working there, so it includes the local equivalent of the Oval Office, the surrounding offices for his immediate staff, the Cabinet room for the more important meetings and formal rooms for official receptions and dinners. The “flat”, which is where they (or the Browns) actually live, is just a relatively pokey set of rooms upstairs.
On the other hand, what was originally built as the frontage of a private residence has become the facade of a whole complex of offices and so the view from the street is now somewhat deceptive.
A townhouse is a house, not an apartment. I’ve lived in townhouses, suburban houses, and apartments. A townhouse, or row house, is a lot more like a suburban house than it is like an apartment; the only real difference is that a townhouse has no front yard and only a very small back yard. Another difference is that a neighborhood made of townhouses is a place where you can walk!
All of this is explored in fascinating detail in Yes, Prime Minister. I strongly recommend the books, in which the stories of the tv series are published as diaries.
Another point which I don’t think anyone has made is that 10 Downing Street is actually two houses, as it’s been knocked into the house at its rear, to make one vast complex. Apparently there is a courtyard somewhere in the back.
Seriously. Big place. Do check out the books.
Really? Now there’s a co-incidence. 
[QUOTE=RossAnother point which I don’t think anyone has made is that 10 Downing Street is actually two houses, as it’s been knocked into the house at its rear, to make one vast complex.[/QUOTE]
I did link to a couple of pages that explained just that. 
That was my first reaction to the OP, as well.
I’ve heard apartments called flats, but I’ve never heard a townhouse called an apartment! Big, big difference.
I’ve always heard them called “row houses” when they’re in a city (like Baltimore), but “townhouses” when they’re in the suburbs (like where I live). I wouldn’t be surprised if the nomenclature varies regionally.
Also, I rent a townhouse, and I definitely have a front yard. Postage-stamp size, to be sure, but I have to mow the grass and there’s a tree and everything.
I think “no front yard” is more typical of a row house.
I think I know what a “rowhouse” is - one house in a row of attached houses. Does a “townhouse” have to be attached, or can it be like mine- a front yard about 15 feet deep, with 3-4 foot wide alleys between the houses? Never heard either one called apartments- I’ve only heard apartment used when there is more than one unit in a single building.
I think the material point is that both apartments and townhouses involve the indignity of sharing walls with strangers.
Tony doesn’t share walls with strangers. He shares walls with his deadliest enemies.
Gordon Brown lives next door (Gordon lives in number 10’s flat which is really quite small as he has only got a wife and baby - Tony lives in the flat in number 11 - which is officially the chancellor’s house as he has more and older kids.)
There are other government homes: There’s a flat over Admiralty Arch (which I believe Prescott has nabbed) and there is Dorneywood, a nice old house out in Buckinghamshire which is in the gift of the Pm - again I think two-jags has it. And the PM gets Chequers - as mentioned above. He also gets a go in Cliff Richards Villa, and hob-nobs in Berlusconi’s holiday home (Tony’s a man of the people you see, not one of them greedy tories.)
The other thing to remember is that our head of state DOES live in a variety of places that are MUCH grander than the White House: Buckingham Palace: Windsor Castle: Balmoral; Sandringham (and if she wanted): Hampton Court; Osborne House; Highgrove; Clarence House; Kensington Palace and so on.
Trust me on this - the Throne Room is more impressive than the Oval Office.
I take it then that I’m the only Doper who has been inside No. 10. And, yes, the bit at the back is rather grander than the Downing Street frontage suggests. But the staterooms are just a set of medium-sized reception rooms of the type you can find in a number of other Georgian townhouses in London. (That bit of the building is actually older but what you see is Georgian, or even Quinlan Terry pseudo-Georgian.) If grand by most peoples’ standards, they’re hardly palatial. But they do include a couple of fine rooms by Sir John Soane, unquestionably the finest British architect of the early nineteenth century. And there’s no real reason why they would need to be grander. I would suspect that they’re adequate for most of the official entertaining a prime minister has to undertake and, in any case, he has access to other, bigger government venues if he needs them.
It also must be remembered that the original reason Walpole was granted the building was as a more spacious alternative to the accommodation available in the royal palaces. Senior ministers had previously been given apartments within the palaces so as to be on call if the king needed them. The choice of Downing Street was not because it was close to Parliament but because it was close to St James’s Palace. For Walpole, getting a large townhouse of his own on a prime site overlooking the park was definitely the better option.
Yet what is striking is not that the prime minister retains an official residence but rather that over time most of the other ministers lost them. In the eighteenth and nineteenth centuries, as personal ministerial attendance on the monarch declined, they stopped being given apartments in the royal palaces. But in the final decades of the twentieth century that trend was reversed. Quite a few ministers now have official residences. Partly this is because a number of historic houses, such as Dorneywood, were donated to the government for that purpose and partly because increased security concerns is always available as a convenient excuse.
Plus the fact that it was only in the twentieth century that it became the norm for prime ministers to live there. Before then most had large London townhouses of their own and so many never used it. Then, as it happened, the rise of middle-class PMs roughly coincided with the rise of press photography.
I wonder if Blair would have left bugs in George’s private rooms and offices?
I’ve only ever seen/heard of attached townhouses, so I don’t know what I would call a house like yours. My townhouse is one in a row of five, but would definitely never be called a rowhouse (for reasons I’m not quite sure of). Is your house shaped like a townhouse/rowhouse (taller than it is wide), only not attached? The image coming to mind is something found in a city, like the Shambles in York; or something out of Dickensian London. As I said, I wouldn’t be surprised if such townhouse-vs-rowhouse naming conventions vary regionally. 
I think my material point is that sharing a wall or two is all that apartments and townhouses have in common. And there’s nothing undignified about living in either type of dwelling, thankyouverymuch.
At the risk of stating the obvious, the American head of state and the British head of state both get big fancy mansions, as the British head of state is the Queen.
We can imagine that a certain amount of the impressiveness/historicity/dignitary-reception duties that necessitate a mansion are the province of the Queen as head of state, not the Prime Minister (or at least, the Prime Minister can employ the Queen’s digs for this purpose when necessary, I’d assume).
To describe the Canadian case, Rideau Hall has all these fancy ballrooms and so forth that Her Ex doesn’t actually need in the course of her day-to-day household affairs: they use them for receptions, baise-mains, dinners, galas, award ceremonies and so forth, that wouldn’t be expected to take place at 24 Sussex. The same could be said of the White House.
I could point out too that whereas the White House contains a whole passel of offices, the Prime Minister’s main office is in the Langevin Block downtown; I imagine he has dedicated workspace at 24 Sussex, but his main office is elsewhere, and the building is more exclusively a residence than either the White House or Rideau Hall are.
Since no one else has provided it, here’s Cecil’s take on it.