Hi there, congratulations on finding a Coventry Eagle with that brilliant sculpted eagle head badge! You're right about the link up with Falcon. Pure guess is that your bike may be early 1970's with that badge. The 90 degree pipes you describe could be pump pegs? (another guess!) We need photos of your bike to give you any real help, with detailed shots of the lugs, frame joints and parts. A clue to the type of tubing might be if the bike has forged rear drop outs with a built in derailleur hanger - they only put these on the higher level frames with better tubing during the late 1960's early 1970's. Flat plate drop-outs with a bolt on claw bracket derailleur don't necessarily mean a lower-end frame, it could be an older model. Parts could be replacements of course.
PLEASE POST PHOTOS OF YOUR BIKE!!!!
My own Coventry Eagle Commodore is made of Reynolds 453 butted main tubes (titanium/manganese/steel alloy seamed tubes), which are very strong and slightly heavier than 531 but for a touring style frame it makes a comfortable ride. It does have forged ends with a derailleur hanger. I think the bike is around 1982 as it has a cheap foil sticker in place of the elegant sculpted eagle on the head tube. It was a lucky shed find that I've built into a commuting bike for my son to use in London, hence the deliberately tatty look, to discourage thieves. Here are some photos, which may be of interest, but really because I like an excuse to show pictures of my bikes!