Remember that in American sports, all the teams are franchises. That is not the case in UK sport, where teams are their own businesses.
Having said that, there is no reason why it couldn't be implemented. There is nothing the EU would do about it, as there is already a salary cap in Rugby Union. Unfortunately as you see in Rugby Union, the best players go overseas for more cash. That's why Jonny Wilkinson is playing in France.
I don't even want a salary cap, I want a luxury tax like you see in basketball. The FA sets a salary, say £80m/year. For every £1 over that you spend on salaries, you have to pay the league £1, so if a team had a £100m/year wage bill, they would have to pay the league a further £20m. This money is then shared out equally to all the clubs under the tax.
It could be done so the money filters down the leagues, to Premiership teams get 85%, Championship 10%, League 1 3% and League 2 2%.
As an example, lets say the amount of tax paid by City and Chelsea is £30m in a single year. That means £25.5m get split between the remaining 18 Premier League clubs (about £1.4m each), £3m gets split between the 24 Championship clubs etc...
Big clubs get to spend what they want, but the whole of English football benefits. Win/win I say.