I'm a qualified mortgage advisor and it's a piece of cake to get a mortgage on a council house BUT it will be harder as you want to buy it in your name. It will be possible but you need to see an independant mortgage advisor to get the best advice. Look in Yellow Pages (and avoid the really big flashy ads - look for someone fairly local, there will be a good few).
Whatever you do DON'T pay more than �695 as a fee to your mortgage advisor as that's more than fair. You may find some willing to do it for no fee, but given recent regulation changes this is less likely, but many who advertise on tele, or even in local papers charge upwards of �3,000 which you DO NOT need to pay.