if the VAT has been paid and not reclaimed, then it will not attract further VAT.
As an example, Mr A buys a defender light utility for work, as a VAT registered business. He (rightly) pays VAT to the supplying dealer. He can then (rightly) claim the VAT back from the government. Usually, this doesn't (although it can) become a payment back, rather than a deduction in the VAT he has to pay in the course of running his business.
He then decided to sell the vehicle on, and to the sale price, he must add VAT, which he passes on to the government. However, the amount of VAT he has to add is less than that he originally paid because the vehicle is now worth less because of depreciation. So he sells the vehicle to Mr B, who again, pays VAT and reclaims it back.
NOW, this carries on until the point where the vehicle is bought by someone (or a company) who is not VAT registered. The have to pay the VAT when the buy the vehicle from Mr B or C or D, but, because they are not VAT registered, cannot claim the VAT back. At that point, the vehicle no longer attracts VAT in any transaction, irrespective of whether the subsequent buyers are VAT registered or not.
When the vehicle is sold, it does not have VAT applied.
(it gets a little more confusing if the vehicle is restored and then the cost of the modifications if carried out by a VAT registered organisation will attact VAT but the original purchase price doesnt).
So, if you didn't pay VAT, or get an invoice which clearly stated the VAT element when you bought it (only if you bought it from a VAT registered organisation or individual), then no further VAT will be payable or chargeable.