Possibly worth a go, but if they can see that card is closed then they would know thats not quite true anyway.
But... Its someone at the end of the phone that you will never speak to again, and so as long as you get the card number it doesnt matter how.
I said "My account was a bit of a mess when I had it and I am trying to see where I went wrong".
Which is sort of true, because where I went wrong was paying ridiculous amounts of charges which I should have questioned because they were unlawful. : )
I did still send off £10 and an
Subject Access Request for both of these, so that I followed the correct procedure.
Good luck