As this is a private sale, the onus is on the buyer to inspect the vehicle and decide it is roadworthy. If you have declared any faults that you were aware of then you have upheld your side of the deal. The MoT certificate only proves that the vehicle was roadworthy at the time the test was carried out, and if the buyer wanted to have the vehicle inspected they should have done so before purchasing, not afterwards.

Although the new owner is taking legal action against you, from the information you have provided it would be quite difficult for them to prove you are at fault. If you still have the text message from them saying they were happy with the car it is in your interests to keep this as evidence. If legal proceedings are instigated it would be sensible to get your own legal advice.