Some notes on navigation:
The distance between things in the British Isles can have a strange warping quality. Cornwall is far further than you’d imagine from looking on the map, as is Scotland beyond the central belt (Scotland’s most southerly point is barely 1/2 way up the British mainland). Assuming you’ll average 50mph is a good rule of thumb for longer journeys.
Zoom google maps in map mode (not satellite) until the scale shows 10 mi. If you can’t see the road you’re planning to use, and it’s near a big (~> 10 mi) gap between blue, orange or green roads then be prepared for roads as described by SanVito - his linked picture is in the apparently road-free gap just below Shrewsbury bordered by the roads to Ludlow and Kidderminster. Some parts of the country are worse than others once you’re off the beaten track - Cumbria and the Dales can get pretty tight, especially if there’s anyone in a BMW nearby.
Don’t get the smallest engined car though - once you get into the pretty bits it can also get pretty hilly in places. For the most part it’s flatter south of the line between the Severn estuary at the bottom of Wales and the Humber by Hull.
Things to see:
Well, there’s London, I suppose, which gets most of the arts, culture & transport funding and its inhabitants then still have the gall to say they aren’t getting enough. It does, however, have excellent museums, theatres etc etc …
Most of the castles are in the bits that habitually annoyed the monarchy and thus got stomped on in the form of rampaging armies using a castle for a base - North Wales and Northumberland/Durham/Yorkshire have the highest density of them; there’s quite a few in Scotland as well, Edinburgh being the most obvious.
Town halls in the north of England. This sounds perverse, I know, but the great northern cities had a mad game of one-upmanship back in the 19th Century, resulting in some of the most spectacular buildings you’ll see. Liverpool, Manchester, Bradford, Leeds, Sheffield were all at it. A few years back I used to live and work in Warrington, which is but a town. They decided to opt out of the game by having some fancy gates put in instead (that’s my theory anyway).
Cathedrals - St Paul’s in London, Ely, Lincoln, York and Durham are those most worth seeing. Note that there is pretty much nothing else of interest in Durham - continue to Newcastle, where there are other things to do.
Ironbridge Gorge near Telford for the first cast iron bridge, Pontcysyllte Aqueduct near Llangollen, the National Railway Museum in York.
In addition to the national parks already mentioned, Snowdonia and the North York Moors are also worth a thought.
Other random thoughts:
Pubs with a 70s or Karaoke night banner out front are usually worth avoiding.
As are motorway service stations, the one exception being near Tebay on the M6 just by the Lake District.
We are currently attempting to make Scandinavians feel more at home by exponentially raising the beer prices. The Cask Marque sign outside a pub means that at least you won’t be paying through the nose for bad beer. You’ll be paying through the nose for good beer.
Beer prices, and the quality and size of fish and chips portions generally improve as you go north. Condiment etiquette in chip shops changes nearly as quickly as the local accents.
I think you should definitely explore Scotland as well as England. The lochs are lovely, and I really enjoyed the small seaside town of Oban. If you are small roads people, you will probably like B&Bs. I have loved the ones I stayed in, with the exception of a real dump in London. 
Besides, we’ve been to Paris a few times before.
