Mortgage- adding parents tax implications?

Hi guys,
I'm a noob so be gentle!
So problem as follows, grateful for any knowledge or advice you can share!

Separated from husband and tried to sell house wih no luck as many have found in these times. Have gained permission to let from the mortgage company and am looking into that no worries. Will be taking ex off mortgage but as I am unable to solely support the mortgage ( apparently though in reality I could if rented, the bank aren't happy to allow that) I'd be adding my dad to the mortgage and herein lies the issue.
My dad owns 2 properties which he lets for profit (neither have mortgages) if my dad was added, would he have to pay tax on my house? It is doubted any profit would be made at this point.

If anyone else has been in this situation I'd be massively pleased with any info!!

Thanks in advance ,
Leiacake