my husband left, and he says i can have the house if i proceed with a divorce, but i cannot take over the mortgage, but i would like his name off the deeds so he wont have any rights to take it from me or sell it.
deeds are mostly irelevant. The lender will have a charge on the property with the land registry. They will agree to you having sole ownership only if you can convince them that you alone satisfy their lending criteria. If you can answer yes to this question then they would probably agree:
Under the lenders limit for lending, eg 3.5 times salary, would they lend you enough to cover the outstanding loan?
The lender seeks to maximize the likely hood of the loan being repaid. With a joint mortgage they have 2 people to pursue.