It is a criminal offence to misuse a BB with max. fine up to £1000.
From what you've posted I wouldn't think that the issuing authority would care two hoots about the matter. Furthermore, you posted:
They have all details from car registration. I have sent the badge back to local council.
The only details anyone has from car registration are those of the registered keeper, which tells them nothing about who used the badge. These details aren't available from your payment because anyone can pay a penalty charge. So, apart from the issuing authority* not being interested IMO they wouldn't know who to pursue anyway..unless you admitted it was you in a covering letter sent with the badge or during the PCN process.
- * are the BB issuing authority and PCN enforcement authority the same?