Apologies for not getting back to you sooner, I experienced some temporary connection issues and could not get back on the site until now. All appears to be resolved now so I can continue dealing with your query.
Generally, when a person places an order for something and pays a deposit (or even pays In full) they enter into a legally enforceable contract with the seller. It is implied that the seller has accepted the payment as security and as proof that the buyer wants to proceed with the contract. I know you are only buying a service here rather than an item but for ease of reference I will refer to you as a buyer. Also I will refer to a deposit but in your case you can assume that the whole payment was a deposit as it would be treated the same.
Unless the seller subsequently commits a serious breach of contract, or there was a cancellation clause, the buyer would have no legal right to cancel the agreement and if they do so they will be acting in breach of contract and risk losing their deposit/payment. This is especially true if the payment was described as non-refundable.
However, if this was a business seller, they will be subject to certain consumer rules and regulations. For example, you will have some protection under Schedule 2, Regulation 1(d) of the Unfair Terms in Consumer Contracts Regulations 1999. It states that if the contract has been cancelled after a deposit has been placed you are entitled to have the deposit returned in full, unless the seller has spent time, effort and money, in which case they can deduct reasonable expenses. Even if some expenses have been incurred, if these are subsequently recovered, for example by selling the item to someone else, the deposit should still be returned in full. It follows that a blanket non-refundable clause that entitles the seller to keep the deposit in all circumstances is most likely going to be unfair and unlawful. For example if they have managed to get a replacement booking for these dates and reduce their losses there should be no reason why they are keeping the money.
If you are having difficulties in recovering the deposit when you believe you are entitled to have it returned, advise the seller that you will not hesitate reporting them to the Office of Fair Trading and, if necessary, pursue the matter further through the county court. Exerting such pressure could often work in changing the seller's position in this matter.
This is your basic legal position. I have more detailed advice for you in terms of the steps you need to follow should they refuse to refund you, which I wish to discuss so please take a second to leave a positive rating for the service so far (by selecting 3, 4 or 5 stars) and I can continue with that and answer any further questions you may have. Don’t worry, there is no extra cost and leaving a rating will not close the question and we can continue this discussion. Thank you