Nice find! I am not very familiar with the German Diamant brand, and I am not really into fixies either, as you may have already guessed. But I do like the purposeful look of vintage track bikes and especially the stories that come with them.
What does it say on the bottom bracket shell? The seems to quite some text. A name, perhaps?
There is a German website dedicated to Diamant, which has a page on (all?) their track models. You might be able to recognize some of the details if your bike is indeed a German Diamant.
There is a German classic bike forum that might be worth a visit: Rennmaschinen bis 1990. One of their members, "martl", also regularly posts on Bikeforums C&V. He may be able to point you in the right direction.
Very interesting - I can now make out "BRITISH MADE" script, a serial number above it that looks like maybe "H 57130" and another stamping in the middle maybe "CB VSTAN" - assuming British Made this isn't a Diamant now?
Any further ideas here? I also looked at the German track bikes and this doesn't look like them, fork crowns and lugs are all very different