We've got a shop called motorsave which does those kind of things, so i would have thought somewhere like halfords should. Bear in mind, you will need to take your log book with you.
You can see what available plates there are on DVLA website if you're looking for a new, personalised one, otherwise if just a new, replacement one then yes Halfords.
The number plates on eBay are from a seller in Scotland, as you do not have to provide your documentation in Scotland like you do in England - their laws are different. So I was told!
I have mine done at a place on a local industrial estate whenever we change cars, as I always need a long one for the caravan and a square one for the trailer. They always ask for proof of address - I take my council tax demand - as well as proof of ownership (log book).