Thank you. If they have sold you an item which is not of satisfactory quality or fit for purpose, then you are correct that under the Consumer Rights Act you have a right to reject it within the first month after purchase and get a refund. This right is not dependent on the manufacturer or anyone else approving this – the seller has a legal obligation to refund you regardless of whether an engineer has assessed it or not. However, even if your rights say that this is what should happen, you cannot force them to act in that way.
If they refuse to resolve the situation, then you would potentially be able to seek compensation in terms of getting a refund or a replacement item. You cannot however claim for stress or inconvenience or charge them rent. So you are looking for actual losses incurred such as having to get a replacement or get it repaired or simply getting a refund if you have not had to get a replacement.
You can still quote the applicable rights you have under the Consumer Rights Act as mentioned above. If they appear reluctant to assist, write to them one more time, warn them that they have 7 days to comply and inform them that if they fail to meet their legal obligations, you will have no choice but to report them to Trading Standards and start legal proceedings to seek compensation for your losses.
This is your basic legal position. I have more detailed advice for you in terms of the steps you need to follow to take this further, 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