Is litigation necessary... Heathrow has plenty of police officers. I've often wondered if you located one, positively identified the property as yours, explained it was being unlawfully held and request they take it into their custody.
The time I was there 2 years ago a gentleman had his wallet with all his cash/cards withheld by them and was explaining over and over that he couldn't pay the fee until he got them back to a women who seemed convinced 'That it ain't my problem innit' (in the end I offered him a £20).
Probably what I would have done in his situation.
But really, don't you think that if you had mislaid your property, that you should be responsible for paying the costs of recovering it, storing it, recording it and retrieving it for you? Why shouldn't meet this responsibility?
Regarding your suggestion of wasting a police officer's time I can't see that working. If it did then the British Transport Police would never get a thing done at Waterloo as they'd spend all their time at the lost property office demanding people get their stuff back without paying for the service.