Hello Angus - it's all a Q of how you are registered. We don't generally register someone as a 'trustee' so I assume you are registered as a joint owner with your Mother after she transferred it to you and her after Dad's death
If that's the case and you are both named as registered owners then you don't need probate as the property doesn't form part of her estate. The legal ownership passes to you to deal with and that can include a sale.
The only issue you may need to consider/deal with is if there's a form A/joint ownership restriction on the register. If so and you are selling then PG 21 section 6 offers guidance on how to deal with the form A restriction -
Practice guide 21: using our forms for complex and more unusual transactions - GOV.UK