I don't live anywhere near Brighton so unsure what the answer is to your question, but I do know that a lot of shops do starter sets for babies if you can't get a babygrow printed - BHS being one in particular. Good luck with it.
Try the Amex Shop. Your only problem being that there is no room on a babygro to fit much of a name. Still you get a nice Club badge on the front. Perhaps just a number on the back, if you plan on having a large family. You have not been charged for this information.