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I would drop it to a Tesco store close to where you found it. He/she probably wouldn't know where they dropped the card/key, but the store would be on/near their commute the next day when they go to pick it up after being contacted by Tesco. And if the person can't be contacted (no phone number on file etc) they know at least which 1000 stores to drop by and ask around, if they wanted.
Not sure where to best post this. Found someones Kryptonite lock key and tesco clubcard on the way to work this morning. Thought I could contact them via Kryptonite, but they don't seem like they do that. Will drop them in to a Tesco tonight. Let me know if you lost them in Hackney.