The archaeological evidence suggests they were abandoned and fell into ruins at about the same time as the legions left Britain. See Fleming's Britain After Rome for a good overview. She suggests that, without the subsidized shipping which supplied goods to the legions, Britain's economy was unable to survive and its elite (and their houses) collapsed.

There's a bit of debate about this, though. Most of the big Roman sites are covered in 'dark earth,' a layer of soil which might be evidence of the sites' abandonment; but it also might be dirt that came from people living in the sites and failing to keep them clean to the same standards as during the earlier Roman period. It's hard to date this 'dark earth' because, after the legions disappeared, you don't see many coins (the easiest way to date something is if you find a coin buried in it) nor diagnostic pottery (pottery made in a style that can be dated, sometimes about as accurately as if you found a coin). I don't expect this debate to end any time soon, so it will remain unclear when exactly the villas were abandoned, though I think it's safe to say that (architecturally) they decline after or around 410.

Another thing to think about is the question of squatters. You frequently see shacks, huts, or wooden structures appear inside villas or other Roman sites. These have been interpreted as evidence of 'squatters' who move in to take advantage of the standing walls to give them shelter inside the crude huts they construct. But some recent scholarship has suggested this 'squatter' activity may have been much more complicated, and might actually be connected with the continuing use of these sites, and not evidence that they were abandoned before being taken over by hobos.

Adam Roger's Late Roman Towns in Britain: Rethinking Change and Decline is a great study of these questions, and is definitely worth a read if you can get your hands on it.

Some Roman buildings were later used as cemeteries. Sometimes this happened after they were abandoned, but in other cases it begins so early that the Roman landowners must have still been present (as at Wasperton, a cemetery begun in and around a Roman structure in the 4th century, which continued to be used through the 7th by the population which lived there through the whole period of post-Roman transition).