I think the general consensus is .... not really. Even the developments ( Southern Dunes on US 27 for example) where the front gate of the community might be close enough to walk to local businesses, the development itself could stretch a mile or more back from the front gate. Unless you know for certain the villa you're getting is right "up front" even the best laid plans might not work out for you. For safety reasons, I wouldn't recommend a lot of walking in central Fl, particularly at night. There aren't very many sidewalks ,street lighting can be pretty average, there are beaucoup de critters (snakes, gators, mozzies) who like to roam about at night , so few people do walk that drivers don't seem to watch for them very much and coming from the UK, you're initial reaction may be to look the wrong direction for on coming traffic.
If you have a strong reason for wanting to be walking distance from those types of facilities, you may be better off looking at timeshare developments (but they'd be shared pools) , even then some of them can be quite spread out as well. Vistana, Bluegreen on 535 , there are a number on the southern end of I-Drive. On property the DVC resorts of Old Key West and Saratoga Springs are close to downtown Disney and Disney is offering some astonishing deals with free dining on them for selected dates.
I'd either bite the bullet and drive (have a "designated driver" ), or look at alternative accommodation, JMHO.