Hi - I've got a couple of bikes from this factory, a 1982 Coventry Eagle Mixte Racer and a 1988 British Eagle Safari Mixte MTB, so I've been trying to dig out the story.
The best information that I have so far is that Ernie Clements (Olympic Silver Medal 194
was working for Roberts Cycles in Birmingham, and wanted to build a new range of quality bikes. He found some old "Falcon" stickers and used them on the new bikes. Then when Coventry Eagle were looking for a better factory (theirs was bombed out), they bought the whole Roberts outfit, including Ernie Clements and the Falcon line. In due course they outgrew the Roberts factory and moved to Barton on Humber, in 1968, where "Falcon" became the dominant name, and Clements was in charge of production.
Unfortunately, none of the other Directors could work with Ernie Clements, so they bought him out, and he took the "Coventry Eagle" brand name in part payment, in 1978. Up to this point, the Falcon head badge included Ernie Clement's name, but changed after the split.
Ernie then persuaded the Welsh Development Agency to get him a new factory in Newtown (where there were skilled bike builders from the old Phillips "Lion" factory at the other end of town). From 1980 he was building good bikes there as "Coventry Eagle", "Ernie Clements" and some for "Barry Hoban". But apparently Ernie had a liking for a lifestyle with expensive cars, and by 1983 his business was virtually broke. The head badge on Coventry Eagles from this factory is a white circular sticker with a garish gold eagle.
Somehow, Ernie persuaded Barry Hoban (another very successful racer and Tour de France winner) to take over the business in 1985. Barry's new business (in the same Newtown factory) was called "British Eagle Cycles Ltd", and built "British Eagle" and "Coventry Eagle" bikes - some were very good, such as the BE "Touristique" - a rival to the Dawes "Galaxy". Some others looked good but were decidedly wonky - like my BE Safari mixte: frame out of line, rear wheel wrongly dished, wrong BB etc.... As delivered, the two wheels left two separate tracks! (Sorted now....)
Ernie Clements left and opened a bike shop in Bromyard.
Barry Hoban's business succumbed to the falling market and by 1990 was sold to the Townsend group, who also bought up the Falcon trading name, plus Claud Butler, Dawes, and many others.
"British Eagle Cycles Ltd" were then re-branded as the very similar "British Eagle Cycles Company Ltd", and soon left Newtown. As a result, questions were asked in Parliament about how much State money had gone into the factory!
Townsend principally imported bikes and components from the far east, and continued to sell all these brands, but on the cheap bikes that they imported, and still do today as the Tandem group.
As I say, this is the story as I have it so far - but any further info or updates are always very welcome!
So far as the original poster's bike is concerned (it's very nice!) - there's a chance that the forks are by Tange - in which case the date is stamped on the stem - eg "82" for 1982. Worth a look!