As long as the contract was concluded on your usual trade premises cancellation rights are not available to the customer.
As the law stands currently, the consumer does not have a right to reject the goods for a refund as long as the goods are ‘of merchantable quality’, ‘as described’ and they are ‘fit for purpose’.
If they have just changed their mind they are not entitled to a refund. Unless of course you have a published returns policy in which case you will need to abide by the terms of that.
However you may wish to make a good will gesture and offer a compromise to maintain the customer relationship. That is a business decision.
The only complication is that the goods were ordered by one party and the balance was paid by another. The law is such that the contract is between the purchaser and the seller and hence the purchaser is the person who can exercise their statutory rights. This would require a little more research to determine exactly who the consumer was in the circumstances described.