Hi Kirstie
Yes there is a Primark in Leeds city centre - if you have access to a map it is on the east side of the junction with New Briggate and The Headrow. It used to be the Odeon Cinema.
...
The TIn Tin is one of the better ones in Leeds. It will definitely not bankrupt you! The decor and the style of the place is matched only by its (not over the top) food. It is in a decent location ...