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 15% of the payout to cover the Peerspace 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 15% of the £200, which is £30. 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 £30 from the £200 before paying you as a host instead of first paying you £200 and then charging you separately for £30.
So even though it seems you carry the full VAT cost of the Booking facing the guest, you should remember that the 15% Service Fee is a sales cost that you can subtract from your financial accounting.