Generally, when a person places an order for something and pays a deposit they enter into a legally enforceable contract with the seller. It is implied that the seller has accepted the deposit as security and as proof that the buyer wants to proceed with the contract.
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. This is especially true if the deposit was described as non-refundable.
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. In this case not only have they not suffered any losses but there was also an agreement that the deposit would be refunded on certain conditions.
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. If you have to go to court then this would be in the small claims court, which is relatively straightforward and can be initiated online via www.moneyclaim.gov.uk.
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