I phoned the airline. They had found it. Getting it back was impossible. It was apparently sent to Helsinki, then back to Heathrow in London. The airline just say "we had it sent to London - ask there. We're done."
Fine, but if you go to LHR and ask where the lost property office is, you are met by blank looks. No one knows. There are 5 4?) terminals, all are huge. Someone says there might be something air side in T3, someone else says there might be something near the car park in T5. Others appear to find the very concept of lost property novel and confusing.
I found one place, but they only did lost property for select airlines, and even then it is not open to the public. WTF?
It pushes me off to know that my tablet was sold off to someone despite spending ages schlepping around LHR trying to get it, having been in contact with the original airline and having it sent to London.