Firt time leaving home and on incapacity benefits! need help and advice

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LHA is claimed from your local council. There is normally plenty of info on their website. There is a form to fill in but different councils have different requirements, for examples some councils you make an appointment to go and see someone to fill it in with or you might have to make a phone application.

You can also claim council tax benefit at the same time - if you get full LHA you would normally be entitled to full Council tax benefit.

To go on a housing list you normally need to prove local connection (ie be living or working in that area or have a close family member in that area) - without local connection you often get a lower banding / points (depending on scheme in operation in that area). Bedsits and one beds are the least in demand properties (I'm assuming same in Sunderland / Durham area) but I think most councils have a high demand for properties these days and you could be in for a wait. That isn't to say you shouldn't go on the list, just be prepared to wait and to have realistic expectations about what you are going to be able to get.
Good luck!