Who will benefit from the rate cut?
This is a difficult question and, as is often the case for VAT queries, "it depends"! This point is in part a legal issue and in part a commercial issue so the first point is to check the contractual position:
In the VAT legislation, there is a provision which states that, where a contract is made before a rate change but the contracted supply is made after the rate change, that, unless the contract provides otherwise, the price is increased or decreased by an amount equal to the change. So, for example, if the accommodation price was agreed on 1 July but the tax point (i.e. earlier of the accommodation stay, invoice and payment date) is on 20 July, this provision applies and the reduction must be passed onto the customer.
However, where accommodation is booked after 15 July, this is not the case. Here, whether or not the reduction must be passed onto the customer will depend on the contractual terms. If your contract or price agreement states £100 plus VAT, you can't charge £120. I am not a lawyer, but would expect that if the contract /booking price says "£100 plus 20% VAT", you would also be obliged to pass the rate change on. In these cases, only £105 can be charged.
Where there has been no mention of VAT contractually, or anywhere else within the agreement or booking price (or indeed the price is quoted as "VAT inclusive" only with no mention of the rate), then there is no obligation to pass on the rate change. This may then become a commercial decision, and of course there are arguments both ways.
I hope the information above is useful, but I appreciate that there will be many questions which may apply to your individual circumstances. If so, please do contact me at firstname.lastname@example.org or 07971642789.