Considering the query was posted 6 weeks ago, my reply may well be too late in your case! Sorry! Normally you have to accept the accommodation NASS is offering. They are trying to disperse everyone out of London because it is expensive to provide accommodation in London. Unless you can provide a very strong argument with supporting evidence of why you need to stay in London, there is little you can do to challenge a dispersal. If you have medical issues and are undergoing treatment, ask your GP to provide a detailed report for you. If you are volunteering with an organisation, ask them to provide you with a letter of support. Stress how important your community is to your well being and mental stability and how badly it would affect you if you were torn out of this environment. If you are receiving counselling/psychotherapy, make sure you get proof of this and an appointment card to show the continuous nature of such treatment. If you do need to challenge NASS support, get in touch with the very helpful lawyers at the Asylum Support Appeals Project: http://www.asaproject.org/