I know you stated a lack of intention to make a daytrip, but I should add that several places outside London are reachable by a train journey of about an hour, in case this had not occurred to you. So it is eminently possible to visit them with about as much ease as visiting the more distant parts of London itself. For example Cambridge and Brighton can both be reached in an hour. If the thought of difficult driving or poor transport links was putting you off, then this is surmountable. Once you are in Brighton or Cambridge they are very walkable. Of the two, if you want to leave London, I recommend Cambridge, because I don't think Brighton is that much fun in October.