Many thanks for your patience, I am pleased to be able to continue assisting with your query now. First of all, I am sorry to hear about the issues you have experienced in your situation.
Generally, when a person places an order for something, be it goods or services, and pays a deposit, they enter into a legally enforceable contract with the other side. It is implied that the provider has accepted the deposit as security and as proof that the customer wants to proceed with the contract.
Unless the provider subsequently commits a serious breach of contract, such as failing to supply the goods or services, they are the ones cancelling the contract, or there was a cancellation clause, the customer would have no automatic legal right to cancel the agreement. If they do so they will likely be acting in breach of contract and potentially risk losing their deposit. On the other hand, if the seller has acted in breach of contract and failed to adhere to any terms or promises made, then you can use that as grounds to try and cancel the order and ask for the deposit back.
Whether the deposit can be retained will depend on what the effects of the cancellation were. In general, the deposit can only be used to cover any actual and unavoidable losses incurred as a result of that breach. It could be administrative costs, some loss of profit, etc.
If this was a business retailer, they will be subject to the Consumer Rights Act 2015. That will make retaining part of the deposit, over and above the losses which they have incurred, unlawful as it would be an unfair contractual term.
If initial negotiations to return the deposit have failed, the customer can consider threatening formal legal action if the deposit is not returned. Sometimes exerting such pressure can have the desired effect in getting at least part of the deposit returned. If they still refuse, then the only way to challenge this would be by making a claim in court. This can be initiated online via https://www.gov.uk/make-money-claim.
Finally, it is worth informing them that they would be expected to mitigate their losses by trying to find a replacement customer following the cancellation. So if they are able to do that, it would mean they have reduced their losses and the deposit, or at least part of it, may no longer be required to cover such losses and should be returned.