I had a similar issue when selling my late father's house. Obviously, my name wasn't on the deeds. I had to provide my solicitor selling the house with details of probate and a copy of his will. It took a little longer than a straightforward sale but not by much. All very easy.
Usually if there was a mortgage on the property at some point it will be joint tenants.
Just, no. That's simple not so.
OP, you need to get a conveyancing solicitor to take a 5 minute look at the title and tell you whether you need to do anything before your mum can sell. If you give them the sale to handle, it should barely affect the overall cost.
Then you'll know that the decision to hold the property as joint tenants or as tenants in common has nothing to do with whether the parties are buying with a mortgage, and everything to do with what they want to happen when they die, and (If they are unmarried in particular) whether they want their share to reflect some unequal contribution.
Although tbh, judging by the many purchase files I have read in 20+ years as a family solicitor, conveyancers rarely seem to grasp the need to advise unmarried couples about this issue. So maybe your comment isn't as surprising as it should be.
Probably if you worked in conveyancing you’d know that it’s practically impossible to get a mortgage if you hold in common, but quite often once the mortgage is paid off people will sever their tenancy. It’s massively uncommon for a mortgaged property to be held as tenants in common, at least in my jurisdiction.
There’s no need to be rude about conveyancing solicitors really. You’ve obviously just come across some bad ones, just like I’ve come across some bad mat solicitors.
We bought ours as TiC years ago with a massive mortgage (because I wanted to do a life interest trust), and the conveyancer didn't raise an eyebrow. Also, a joint tenancy can be severed at any time, not only when the mortgage has been redeemed.