So he was investigated by the Police in 2016 and the CPS decided not to prosecute him.
Of course his defenders are saying why sack him because he did nothing wrong (criminal).
I think the more pertinent question, is why sack him now?
As I mentioned before you do not have to be guilty of a crime to be sacked, reputational damage is a justifiable reason for sacking someone e.g. an inappropriate relationship. So what has changed since 2016? Why did they not sack him then?
If he does decide to sue the BBC I expect his defence will be that the BBC looked at all of this in 2016 and decided nothing to see here. If there is no new evidence he may have a case, why did the BBC change their mind.
From the BBC's POV one reason why things may have changed is if he lied to the BBC back in 2016 and this has now come to light e.g. I never met the person don't know who they are and then proof of contact has now come to light or something like that
None of this requires a criminal conviction just that the BBC is satisfied he has not been truthful.
We shall see.