Can you help to identify these frames, bikes or parts?

I had a pair of these. The cleats has a allen bolt with a spring connecting the two half of the cleats.

Anyone have any clue what cleats these pedals are supposed to take? They are on the spinning bikes at the gym I just joined - the gym claim they are for Shimano SPDs, and they are the right sort of size but as you may be able to see from the photo, they don't have the same structure as a normal SPD pedal so they don't hold the cleat in and you just unclip to the left or right as soon as you start pedalling - there's really nothing to lock them in.
Had a look at previous SPD pedals (the bikes were bought in 2003 seemingly) but nothing seems to fit this spec...