I think mutual exchange or home swap is best option for you. The transfer list will take years and years as you are adequately housed.
Your flat sounds relatively desirable believe it or not - ground floor is a major asset and a small purpose built block is also sought after.
I don;t know what part of London you are in, but ground floor one beds are much sought after, usually for elderly and others that can't manage stairs.
You would have to expect a move to 1st floor and above but that might be worth the swap for a 2 bed.
Speak to the allocations officer (and housing officer) in the landlords/council office as they might know of tenants waiting on transfer list for a ground floor (usually because of mobility probs and they are currently 2nd floor or above). They could put you in touch with them to see if they are interested in swapping.
Also, view your flat in the same way as a seller would - make your flat as nice as poss internally, maybe redecorate, new carpets if you can stretch to that or at least get them professionally cleaned, de-clutter etc so it looks nice to a potential swapper.
Consider a financial incentive to a potential swapper, what is that second bedroom worth to you? Payment after tenancy swap agreed and you have moved.
and then advertise your flat - obviously, you don't give address just postcode, general area and your phone number - advertise GP surgeries, local PO, local shops, tescos etc - anywhere where an elderly person might see the ad and want to contact you - take normal precautions if any swappers come and look e.g.have someone else at home with you.
sell the flat/area etc.
also be open to moving out of your area, keep an open mind
good luck