I bet they have some friend or relative they mainly live with, but once spent a night stuck at Heathrow waiting on a flight and decided to go for a meal there and did it again a few times. They could be hoping for publicity to generate a charity fund to buy them a house or something - its amazing how deluded some people can be, and a lot of their "situation" indicates they are very deluded.
The bit about her constantly turning down jobs I believe though - I know a few people like that, who constantly bemoan the fact they can't get a job and are desperately trying everything, and who apply for jobs all the time, but when they do actually get offered a job, turn it down because its too far away, or the hours are too long, or something.
But I do think this couple should be awarded the "BabyBoomers of the Year Award" or something, just for having failed to buy themselves a retirement home, mortgage-free, when he was 61, with £200,000 in cash.