What other places? You are overthinking it, just bypass the tills and go to the bogs surely, I don't know of a single place in the city centre that has a code on the doors like they do at some takeaway places in Leicester Sq in London, a code you only get on a receipt.
If I was at that end of town I would be going in the Bankers Draft. No need to even inform the staff what you are doing, they likely don't give a toss and far too many people in there for them to notice, just head to the stairs and go down to the toilet. Granted you can't do that with a child past a certain time though.