I remember it well, especially as the Astoria Finsbury Park. Saw some great concerts there, my first Duke Ellington concert (absolutely electrifying), Art Blakey and more. As the Rainbow I think I only saw Miles (offensively loud) and the electric Return to Forever.
As a cinema it was magnificent with a Moorish interior. I believe it was listed as a historic building. Unfortunately it was deteriorating badly last time I was there.