This is correct. As the importer of the goods, you will be charged UK VAT when the goods enter the UK. Some suppliers meet this cost on their customer’s behalf, particularly where they know that the customer can’t recover VAT. But unless they specifically say in their terms that they will, the default is that the customer pays.
In theory, it’s the same as when you buy goods from a business in the UK – the UK seller would have to charge VAT, which is passed on to HMRC.
The only potential difference with your particular example is that within the UK there is a “margin scheme” which allows second hand dealers in some cases to just calculate VAT on their markups, rather than the full price. This scheme wouldn’t be available to an overseas dealer.