I am sorry to hear your having to going through this, any professional will admit when they are at fault (mistakes happen).
To clarify I am not a lawyer so can not offer legal advice, however as a professional myself I am aware that some (cheaper) professional indemnity insurance will not cover old works when you change policy, normally they put a constraint that works done so many weeks before the policy starts are not covered.
That said it should not affect you, as the insurance is to protect the plumber not you, if he isnt covered, the liability still sits with him, if his work is shown to be substandard.
My advice would be to get a formal report back from the AA confirming what they found to be the fault, and what was done to fix the issue, this is critical if you want to take things further.
Washers do tend to bind together so it is possible when the original plumber put the pipe together he didnt notice two were stuck together (but you wouldnt do this on purpose - if you did its a bodge not a fix), what you need to determine was if this was a slow leak (like a dripping tap, or a stream of water), as the argument may be some damage may have been avoided if you had noticed water on the floor.
In conclusion, good plumbers will guarantee their work for over 6 months (most a year), I think you have a reasonable prospect to claim against the original plumber, if you can get the AA to put their findings in writing and get the original plumber to confirm in writing they installed the faulty valve you have a straight forward case for Money Claim Online (small claims court).
Please let me know if you need anything clarified.