Can't help with a house swap, but a very central hotel, albeit basic, is the Travelodge on Drury Lane. They call it Covent Garden.
Depending on what accomodation they need, they could book a family room. This would give them all a bed in the same room. Request a high floor (12 or 13), in the tower, west facing.
http://www.travelodge.co.uk/search_and_book/rooms_rates.php?hotel_id=318&from=listIt works out to be about £95 for the room, per night.
I doubt that you'll find a better price in this area.