If it is a government-issued document and it was not located in the immediate presence of OP, I cannot imagine that BA would turn the document over to BAA for handling in the ordinary course. I would presume that the document was returned to the issuing agency, wherever that might be.

That agency will take whatever action is necessary and apparently replaced the card. OP should drop this given that: 1) he chose to leave it behind; 2) he was admitted to the UK; and 3) the card has been replaced. He should count himself lucky that the card did not fall into the wrong hands and allow the entry of someone who should not have been permitted entry.