So, you will need some kind of proof you aren’t trying to register a vehicle you have just nicked and took the plates off.
If you are buying from the company that bought it new, and they are some proper company registered as a business. Then you could be ok with a headed letter from them saying they bought it new on xxxx date and it has never been registered.
It is pretty unusual for this to be the case. Any motorised vehicle used on a public road, including things making the road need a registration number, unless you are the Queen. When new it could have been registered as a “road mending vehicle” it would be taxed at nil rate and probably mot exempt. So, companies don’t have many negatives to having them registered.
You need to look at form v55/5 to see all the info you will need to fill in, you will also need the certificate of conformity, unless it is old enough not to need one. If dvla aren’t happy with the info they will let you know.
You will need proof of age of vehicle.
Mot
Insurance
Proof of ownership
It is taking some while to get registrations processed at the moment.