There are unfortunately going to be more and more of these cases as council housing stock ever increasingly dwindles and new build stuff is generally 2 to 3 bedrooms.
There are schemes to do lateral conversions etc to offer larger sized properties but these do not become available often so more and more Councils will have no choice but to turn to the private rented sector to rehouse these families that they have a 'duty' to . That means paying market rents and ?1600 a week in central London is fairly average for that sized property.