I think Scott touched on a key point earlier. England may not be as compact as Scotland, but there are certainly more motorways to allow you to cover ground quicker.
I think someone could fly in to Heathrow and spend 7 to 10 days covering the London heathland courses and the Kent coast and leave a happy man. However, I'd probably recommend some travelling, if only to show what the rest of England looks like, but there are so many options. The London, Kent coast, south west combination mentioned is probably the best bet, but there are more than enough alternatives in the Midlands, the north west coast, Yorkshire etc.
Maybe for variety, after the London and Kent coast instead of heading south west (my turn to be sacreligous as a Burnham member), loop north to play some of the following over a few days: Royal Worlington, Brancaster, Hunstanton, Woodhall Spa & Notts?
Cheers,
James