Professor is not a protected job title afaik.
So it's iffy, but not illegal to use it, like saying you are a lawyer. Lawyer is a generic word and not regulated, so anyone can say that.
Solicitors and barristers and paralegals are regulated.
If she was claiming, for example, that she was a school teacher, then that's a regulated profession, and she would be on more dodgy ground.
I suppose an approach could be made to one of the named institutions to ask them to clarify her status.
UK regulated professions and their regulators - GOV.UK
I don't know if her use of Professor within a tribunal setting could be deemed misconduct or malfeasance in a public office, it's a high bar to prove that.
Especially if her defence was that no one ever asked her for evidence of her Professorship, or told her that using it wasn't on.
But the cat is out of the bag with her now and the rest of us know she's likely to be a phoney.
As for the Judge, it's possible to raise questions about her behaviour, often it's used as a way to take matters to appeal.