During the 70s and 80s, despite having only two top twenty hits (NKIT & HC), the Eagles were one of the most played bands on UK Radio. Probably more than the 60s bands, The Beatles, The Stones and The Who, definitely more than Led Zep. Mostly tracks from the 1972-75 Greatest Hits album.
When the charts and Top Of The Pops disintegrated, the classic rock bands got played a lot more and the Eagles fell from prominence. They are obviously still loved by listeners who heard them in the 70s but they don't get much airplay now.
The UK's leading media organisation, the BBC, list their top 100 artists each week, based on the number of plays on their various stations.
The Eagles may make the lower reaches, if a member of the band is in the UK on a promo visit but even when the band itself is in the country, they rarely make the top 100 artists list.
BBC - Music - Artists
http://www.bbc.co.uk/music/artists
Radio plays don't count for much these days but the Eagles don't show up much on other media outlets either.