If you're classed as LCWWRA (sickness benefit element of UC) then you can study an OU degree, as it is considered part-time, however loans or grants you receive may reduce your benefits if you're also earning close to or above the work allowance income, so double check about this. If you're on UC which is a version of job seeker's allowance, I don't think you can claim and study part time, but this is a new benefit so it is worth checking. Try the Citizen's Advice Bureau.