If a reed goes that flat so quickly, Philippa, there’s a good chance that it has failed. With a failing or failed reed, if you tune the reed, it soon goes flat again and is a lost cause. It would be interesting to see photos of the reed from a couple of angles. In trying to “flatten” the reed (in the other sense of “flat”), you probably closed the gap (i.e., the distance between the reed and reed plate, which should be roughly the same distance as the thickness of the reed and should look about the same as the gaps of the other nearby reeds). If the gap is too small, the reed will be less responsive or not play at all. I recently posted “Gapping 101” in the “Melodica Construction, repair, and maintenance” forum.
If the reed has creased, it’s hopeless. If not, here’s what I would do: (1) See if you can get the reed to play by re-gapping it, which will probably involve carefully opening the gap as described in my post. If the reed then plays, (2) try to tune it as described in Daren’s “How to Tune a Melodica” tutorial.” If this is successful, there will still be the question of whether it will hold its tuning. If not, then the only viable alternative is to replace the top reed plate. The P-37D has three reed plates. It sounds like you were quoted the price for the whole set. The top one alone should be about 15 quid. This information is given with a phone number in the first post by Daren in this thread.