Hello, my name is Jim and I am a qualified lawyer happy to help you today.
I dealt with a similar question a while back - Booking.com are hoping you will not bother to pursue them.
According to companies house they have also dissolved their UK address, hence the reason why you have not heard from them. First of all if you paid by credit or debit card you can see if the card company/bank will reimburse you. If your credit card company or bank cannot help you should sue Booking.com. They should have paid you by now especially as they have told you they would do so.
You can use the European Small Claims procedure in order to claim. This allows for cross border claims of up to 5,000 euro in value. You need to fill in the attached Form A and attach any evidence you wish to rely upon to :
County Court Business Centre, PO Box 527, Salford, M5 0BY
The form asks for your bank details and the 25 euro issue fee will be deducted but added to your claim sum.
The court will then serve the form on Booking.com who then has 30 days to respond. The court will consider the response and give judgment on the claim (or if further details are required the court will write to either party). They may hold an oral hearing (by telephone if the court has the facilities - which most do have) but with the facts of this case it is unlikely as it should be capable of being dealt with on paper. If you win you get a certificate against Booking.com which means they must pay your claim.
For reference, and for the Form A, Booking.com's address is:
Booking.com, Herengracht 597, 1017 CE Amsterdam, the Netherlands.
I hope this helps - if you can please click 5 stars at the top of your screen, I can answer follow up questions at no extra charge and Just Answer will credit me for helping you today.