Booking.com is based in the Netherlands, so when they charge you their commission, they don’t add UK VAT on the invoice.
However, under the reverse charge rules for cross-border services, if you’re VAT-registered in the UK, you’re required to account for the VAT yourself.
That means you must declare the VAT on Booking.com’s invoice in your VAT return as both input VAT and output VAT.
Output VAT: You treat it as though Booking.com charged you UK VAT (so you declare it as VAT you owe).
Input VAT: If the expense is related to your taxable business activity (which it normally is for accommodation providers), you can reclaim it in the same VAT return.
The net effect is usually zero, but you still have to record it properly.
If you’re not VAT registered, you don’t need to do anything — but you also can’t reclaim anything.