arfabe, I can only speak for Manchester United fans, but far and away the majority United fans could care less about England (and yes, I'm talking about the English United fans, not the United fans in other countries). Club Before Country is the cry. Some songs/chants heard round Old Trafford include:
"That Boy Ronaldo, Makes England look ****e" (reference to WC06)
"We all know United are better than England"
"You can stick your f'ing England up your arse"
"Did you cheer when Beckham scored" (from years past when English fans were beyond obscene to him when he was with United, but then cheered him when he played for England, like the hypocrites they are).
Most United fans still root for England over other teams, but ultimately don't care and aren't really vested in it. I kind of get the impression that the most passionate England fans are those who support small clubs, especially non-premiership clubs, as England is their time in the limelight to follow something big. I could be wrong, though, but it's just an observation I've made.
I realize this isn't necessarily common with most countries. Maybe it's an English thing. I'm reminded of something that Simon said during the American Idol auditions (the only time I watch the show, for the comedy of it). He said something to the effect of, "What really amazes me about this country is that you are genuinely happy for someone else when they do well."
As a side note, I also preferred club before country when it comes to hockey. I hate when Wings players take off during the middle of the season for the Olympics, as it makes them more tired down the road. Slava Kozlov was always a bit of a hero of mine when he declined to play for Russia in 98 because he wanted to stay healthy and focused on the Stanley Cup.