Auction final price

[StiffyByngsDogBartholomew]

I'm looking at purchasing some furniture in an auction at a local hotel that is being refurbished. Can someone just confirm my understanding..
the site says fees are as follows:
"Commissions*: 22.00% ex.VAT/sales tax
VAT/sales tax on hammer: 20.00%"

so if I buy a bed at £10 after commission it's £12.20 and then VAT is payable on the £12.20 at 20% making the £10 bed's total price £14.64 ?

In a previous life I bought cars from auction for work
it would be

no vat on the price (unless there was, but that’s a car quirk!)
commission
vat on the commission
any fees for internet bidding or additional checks
vat on those fees

it always cost a good chunk more than expected