you'll have to re-read your policy. you say it should pay out on redundancy, so why is it now dependant on sickness?
you could make a claim for Jobseeker's Allowance and they will consider paying the interest on your mortgage. the ESA people can only consider your claim on the basis of their own doctors. if you have had a benefits decision letter, does it say you can apply for a reconsideration, or appeal? you have to do something now, if you have no income. CAB (or other welfare advisory body) can advise you.
best of luck.