I’m looking at my London Tube Map and I wonder how long a morning commute would take from Amersham waaaaaay out at the end of the Metropolitan Line to Holborn in north central London. I picked that one since you’d only have to change lines once at St. Pancras onto the Picadilly Line. As the crow flies, it’s 23 miles.
So how long does this take for the morning rush and how does that compare to, say, midmorning?
Well according to the route-planner at www.tfl.gov.uk it would take you just over an hour if you caught a tube now.
Leaving at 8am makes no difference in the traveltime
According to the Transport for London Journey Planner it takes about an hour both at roughly 7a.m. and midday.
[EDA] drat you delay in preview 
It’s been a long time since I commuted into London.
I note that changing at Kings Cross/St Pancras involves changing levels by escalator, and that in the rush hour everything is much more crowded (you might even miss out on one train)
I remember that Holborn was pretty crowded too. But most crowded during the morning rush. I was in St. Pancras/Kings Cross twice and it was not so crowded as to be inconvienant. But I was on vacation and didn’t really have to worry about being late.
Commuting into DC at 10 is certainly easier than at 8:30. Maybe not faster on the train, but faster for the pedestrian parts like navigating the stations.
I’ve always found TFL to be… optimistic, shall we say, when quoting journey times. They do have the caveat that what they quote is “average journey time” but in general, I add about 25% to their estimates to be on the safe side.
I’d get out at Euston Square and walk.
Actually, Amersham may be served by the tube, but it’s actually not in Greater London at all - it’s in Buckinghamshire.
In general, on the Tube you should allow two minutes per station plus five minutes per line change. This is surprisingly accurate, even over long distances.
Transport Direct, which I think is quite a nifty site, suggests 55 minutes or 59 minutes or 1 hour 2 minutes, but it’s those crowds of blasted other commuters that will upset the best laid plans. Grrr. 
I’d suggest more like 4 minutes per stop once you’re onto the outer reaches of the Metropolitan line. It’s certainly a better rule of thumb on the eastern end of the Central line.
Mornington Crescent, anyone?
Oh dear. Should have seen that coming a mile off, I suppose:D
Since nobody’s quite said it explicitly, the factors involved in why the journey time doesn’t change significantly through the morning are:
[ul]There’s a drop-off in the frequency of trains outside of the rush hour, but during the day this isn’t sufficiently great to make much difference. When you change to the Piccadilly Line at Kings Cross you might expect, say, a southbound train every couple of minutes at peak, but only once every five minutes at midday. On average, you lose a couple of minutes off-peak waiting for that train. (This is a much more significant effect late at night.)[/ul]
[ul]Once you’re on a train, it pretty much takes the same time to get from A to B regardless of the time of day. Given the usual uncertainties of the service. Outside of peak, you are more likely to find the train held “to regulate the service”, but that’s fairly random and usually only a few minutes.[/ul]
[ul]Conversely, as noted you can get through busy stations faster outside of rush hour. (Though commuters do at least usually know what they’re doing and where they want to go. Off-peak passengers are less likely to.) But, again, it’s only a couple of minutes difference.[/ul]
For the sort of journey the OP has in mind, the time spent on the first train to Kings Cross is the vast proportion of time. The interchange and waiting times are just noise on top of that essentially fixed duration.