VAT is a purchase tax applied by the country that the purchaser lives in. Check your local country VAT rules.
The seller does not collect VAT in the UK if it is a private seller, so the purchaser pays the vat when it arrives at its destination according to the local rules. If the buyer is in the UK then there is no VAT to pay, as second-hand goods do not attract VAT on a private sale.
If buying from a dealer, even second hand goods are vatable, as stated above the dealer charges that VAT and passes it on to the UK govt. If the dealer is selling outside the UK he can sell ex vat and make it clear to the UK govt that he has done so, and then he does not pass any VAT collected to them. If you are in the UK and you buy from second hand from a dealer you pay the full price including VAT.