When did you buy?
OK. you do have to prove that a fault exists before you can access the right to reject under the Consumer Rights Act. That is the point that the solicitor is making and that is right in law.
Once you get over that hurdle though you would be entitled to reject.
This will turn upon the issue of whether you can prove a fault. I suppose there is no way of doing that without incurring cost.
If you aren't prepared to do that then their offer of a repair might be an option.
Can I clarify anything for you?