If you are VAT registered, you will need to provide a VAT receipt to your guest directly upon request.
The guest can request a VAT receipt for the full amount paid by the guest despite Peerspace subtracting the service fees. Here is an example to explain why:
If your cost per hour is £100 and the guest books for 2 hours, your sales are worth £200. If you have included 20% VAT in the price, the VAT value of that is £40, which is what the guest can reclaim if they are a VAT registered company.
Peerspace charges the host the service fee on the £200. This amount is a separate transaction (sales cost) between you and Peerspace and is not directly related to the sale between you and the guest. From a tax perspective these are two separate transactions, but for ease of service Peerspace simply deducts the service fee from the £200 before paying you as a host instead of first paying you £200 and then charging you separately for the service fee.
So even though it seems you carry the full VAT cost of the Booking facing the guest, you should remember that the Service Fee is a sales cost that you can subtract from your financial accounting.