No he doesn't Marpleexile,
He only visits London, he works and lives in his Hazel Grove constituency. At least that is what he told us before we elected him. As I recall he made a big issue out of being 'local.' If he had told us he lived/was going to live in London, we wouldn't have voted for him.
Well he did, he was a local school teacher. He's now got a new job based in London, so it's not entirely unreasonable that he might relocate to near where his new job is.
Certainly, as a tax payer, I'd rather be paying his expenses to make a return trip to the constituency once a week instead of making a return trip to London 3/4/5 times a week.