Look at form 'Rent1' it states -
Mortgage Interest Relief (TRS) - if at any point you have a mortgage and are in receipt of Tax Relief at Source you should advise your Local Revenue Office immediately as you may no longer be entitled to Rent Relief and your Tax Credit Certificate might need to be adjusted.
From this i would expect that you can not claim both if you are claiming TRS on a mortgage, You can claim if your paying for private rented accommodation used as a sole or main residence. The term 'Sole and main residence' is also applicable to your mortgaged home and therefore you cant have them both.