The TSA has nothing to do with Heathrow where it was found, though. (I don't think in the UK anyone can be fined: if there's any belief of malice, you're likely to be dealt with under normal criminal law such as conspiracy to murder, or potentially terrorism related offences; if there's not, you can either surrender your property or return landside).
A criminal conviction could lead to a fine.
Well yes, but you couldn't immediately receive a notice with a significant fine.
The OP's point was: they either think you're trying to bring down a plane or they don't. Punishing minor infractions is not on their menu.
Except for drug offenses
Almost: the important point is they have no right to impose any fines; any punishment will be done by the British Transport Police in accordance with British law, and there are relatively few crimes of possession in the UK (drugs are an obvious one, but even then a first arrest for Class C drugs is typically dealt with by means of a police caution). Essentially: any punishment arising from a security checkpoint would be a police matter, and have nothing to do with those manning the security checkpoint.