Not been to the new market either, but we used to visit the old Open Market every week.
Good website in that link, often find myself looking things up.
Marshall's Row, that does sound familiar, I have got a few books of old photos of Brighton, may have seen it in one of those.
Used to say the same about London Road/ Western Rd.
Very rarely went to Western Road as a kid it was London Road as it was full of decent shops and the Open Market.
Most people over a certain age that grew up in Brighton will still call it a town.