i've just done this.
You'll need to insure it and MOT it on the VIN number, Phone the DVLA and get a V55 form for new registration. You'll also need a certificate from the land rover heritage centre proving it's age. Can't remember the cost (around £25 i think), I did it through their website. You get all this including proof of ownership, which might just been photos and documents referencing the fact you've had it for a few years. Send it all off, and then keep resending it after correcting the mistakes they send your forms back. Oh and the cost is £50 or something for the form, and then you have to also pay for Vehicle duty. Then you get you're V5 and can get plates.
Word of warning - Either phone or talk to someone at the DVLA, do not use postal only. I have huge problems waiting for responses, but then phone and got someone's email and the whole thing went much quicker.
https://www.gov.uk/vehicle-registration/new-registrations