For the record, it's Cotswolds and Lake District. Edit: Steve's changed his post again.
The loop in the previous post is trite and will show you only what all your neighbors have also seen.
Cornwall and Wales are sorely neglected by American tourists, but offer some of the best of the UK.
London to Land's End is an easy trip with only two-half days of driving (even hugging the coast which is a much better route), leaving plenty of time for exploring.
Getting back to Cardiff is only four hours or so, again leaving plenty of time to poke around.
Now the question is why just do south Wales? If you make a clockwise route around coastal Wales, the driving time is roughtly six hours (skipping Anglesy and Pembroke - Fishguard) to Conwy and takes you by the best castles in the world. You could do it in a couple of days.
From Conwy back to London is a five hour sprint with not much to see -- unless you maybe spent a half day in the Cotswolds after all.