As far as I remember,all Primark goods are "own brand" and therefore all carry a Primark label.
This means that without a receipt they can tell that they ARE Primark goods.
All well and good.
However,it does depend on WHY you want an exchange(they are not obliged to do so if you just don't like the goods).
Also,it must be obvious to Primark that the goods have not been worn.
I have never had to exchange anything from Primark so these are just the thoughts off of the top of my head,but I have always had good & pleasant service from them,so I cannot (personally) see any problem.