Certainly. This is going to be my personal taste though and areas I tend to know better, so somewhat biased! Ideally you need to look outside the M25 which is a motorway that basically encircles London, but somewhere with good rail connections into town (aka London). You would need to be further out, west, than Heathrow, which is very overdeveloped with housing, but it's not so bad around Gatwick airport if you are using that as your arrival hub.

I would look towards Surrey or Hampshire to the south /west or towards the Cotswolds (Gloucestershire) to the west. I love the New Forest area (south Hampshire) and the cities of Winchester or Salisbury. Oxford is also within the range. I don't know too much about north and east of London.

The three towns I have mentioned are all fabulous with loads to see. Real England with glorious country side on the doorstep. If you have been to UK before you have probably 'done' Bath. Lovely but way too touristy these days.

Hope this helps, or maybe hinders!! Please ask away if I can be of more assistance. I'm not much good geographically north of Birmingham or east of London, but know the south and west of England well.