On 35k you would qualify but you should check if a bank or the council would give you a mortgage with your income mainly coming from SW payments. You are generally supposed to be in fulltime employment for 6 months to qualify.
Have you considered applying for social housing? I don't know much about it but I would have thought that with 2 children you'd be a priority. There is probably going to be a greater supply of social than affordable housing over the next couple of years. Might be worth putting your name on the list while you are considering your options.
Thanks for the reply cheeus. I've been on the social housing list for 6 years and have been told it'll be another 10 -15 years before i get to the top! Its a joke it really is..
You should appeal that to your local authority on the back of having a disabled son. By the time you would qualify otherwise he will probably be grown up!