Hi, I recently settled with my employer, however I recently went for another job and the interviewer had done some background checks (as they do) and they have managed to un cover reasons I settled. He has given me 2 sources, of which both still work from

settled with. Is there a way of proving breach of contract?
We came to an agreement as the company found me in breach of Competition law...In short there was a no of emails which I was unfortunately CC'd in and didn't report.

We came to an agreement which was fair however since this, the employer has been running internal courses on Comp Law and has advised staff that people have lost their jobs because of this... This now puts me in an awkward position as it is a large company and a small industry...Anyone doing any back checks with colleagues are hearing about me 'getting fired because of comp law'

Do I have a case if I go to sue?