Yes Joe, you're right.
Although I'm sure Barnet Homes wouldn't throw Joseph out onto the street without offering other suitable accomodation first, ie a 1 bed.
As I said before, joint tenants though are legally allowed to succeed (if there hasn't already been a succession). So becoming a joint tenant would give Joseph the legal right to succeed.
I also agree with Harry Lime. We're no longer in a position where properties can be just handed through families like they were in the 60's and 70's. So it's a landlords responsibilty to make sure that any claim for succession is real.
Also Joseph, just out of interest why would you not move into a 1 bedroom property? This would free up the 2 bedroom for a family to enjoy it like yours have for so many years?