I am sorry for your loss. This is an awkward one, I am assuming there was no life cover in force, the bank will not be able to just change the name on the mortgage, they will need to do a new mortgage in your name and clear the existing one. Are you working? is there any reason why you would not qualify for the mortgage needed although it is in their best interest to grant you the mortgage if you are already paying the repayments anyway.
Best to talk to them to see what their policy is going to be in this case, then you can decide how to proceed, you may need to get further advice depending on their attitude.