In general you have about a year to get grant of probate & the house can't be sold until you have that.
Until then, the mortgagee will sit tight & wait. Interest still accrues, so they are not losing out.
The mortgagee has 2 years from date of death to start proceedings, before it becomes statute barred.
So lets say they do so at the last minute. It'll still take around six months or so for them to get an order for repossession.
Of course the OP doesn't want that to happen, but thats why I estimate that they have a bit of time to get their strategy sorted.