V5c registration advice, bought a vintage moped with no paper work, and the plate doesn’t match my vehicle???

Recently bought a vintage moped that has no paperwork at all, has been imported here to the east of England from France. I bought it under the assumption that applying for a V5 was just a form I needed to fill in but after running the plate that it came with it comes back as a completely different vehicle. Should I be worried? I’m concerned that the bike should have been destroyed at some point but wasn’t and was sold later, it’s been through many hands without anyone having done any paper work and I’ve just sunk a load of money into it and if I can’t get it registered I’m extremely fucked.