To allege that you are or were an associate of anyone is hardly a case for a libel action (Unless the alleged associate was named Hitler or something like that!). I am sure her lawyer knew exactly what she was doing when writing to you. You don't get to be a member of Matrix Chambers if you are not recognised as at least quite good at your craft. Having been called to the Bar in 1997 and specialising in media and information law, I think you are on a sticky wicket.
She is also recognised as a leading light in defamtion law. What are your qualifications in this tricky area?
Given that the lady in question was/is backed and funded by some big money organisations who may perhaps see their own reputations under attack from yourself (by association), I know where my money would go in the betting stakes if it came to you vs those organisations.
Personally, I think this thread has become the most vitriolic I have seen in a long while and I am baffled why you persist with this virtual crusade.
Why not just give it up as you are creating the view that you are determined to cause as much damage and distress to this lady as you possibly can?