If you have a unique tax reference here in the UK, then you will find once logged in the online NOVA form. If you have the paperwork from the EU country it takes as little as a few days.
Strangely, each EU country has different paperwork, a vehicle from Holland needs a deregistration and export certificate, any modern car dealer can do it. Fiat, VW, etc even for classics, and takes minutes for them to do and print the paperwork.
A relative has just done this, drove to Holland, bought the bike went to dealer with Dutch owner to get paperwork, declared when arrived at customs on the UK side of the ferry route, given a number filled in NOVA and riding it in less than 7 days.