Bloss, £2000 will NOT cover him for a whole month in London unless he dines out at McDonalds every night. If he is lucky he could bag a room at the Travelodge within the former County Hall, which is the cheapest decent quality hotel I know of in Central London, but when I was putting up some Estonian visitors on a similarly tight budget a few years ago I found it immensely hard to get acceptable accommodation for under £100 per night.
He might want to consider a B & B in a pleasant suburb such as Twickenham, Kew, Blackheath etc. We moan about transport but travelcards are still economical....He could also look for accomm near a university campus in the capital as they often have at least one acceptable B & B nearby, for parents at graduation time.