Doesn't BA have an office somewhere near Victoria or elsewhere in London? I ask because the MAD passenger (mad, I bet!) may well be in London and by taking the bag to BA they can look up the record and call him/her to see if they have the OP's bag and just haven't had reason to open it. It would be so easy to return it to someone maybe even at the same hotel!

If I did the act of taking the wrong bag (why, oh, why doesn't everyone have some identifying tag on their bag so they don't do this? The lovely bright yellow FT tags maybe?), I would feel obligated to correct my mistake immediately - not tomorrow, not later, NOW. If for some reason I could not do it personally, I would hire a courier to get the bag to BA. It was the OP's mistake and he seems to expect BA to take care of it or to be able to correct it at his convenience and at the inconvenience of the other passenger. Just a shameful attitude and one that makes me hope judges in his court are not required to be lawyers (some here in the US aren't) as I don't want to be associated with people like him! I also hope he gives parties in his court the opportunity to serve their sentence, pay their judgment, whatever when it is convenient to them to do so because that is the example he is setting!

Rant done. Just take the bag to BA now and be done with it and feel decent that you've done the right thing and even a bit self-righteous if you want. Just do it!