Not surprisingly, England failed to qualify for Euro 2008. They should just simply accept that they are not good enough. Blaming the failure on the huge influx of foreign stars is clearly out of the line. Neither will imposing a cap on the number of non-English players will help. I agree with Arsene Wenger in this case.
For one, the English team have never been great. Before the EU single market that revolutionized the football transfer market in the early 1990s, when there were only three foreign players allowed to play, England never won anything except the 1966 World Cup (the only trophy they have ever won). So the number of foreign players in the English League can not explain the national team's performance.
And remember, the EU open labor market also applied to the other countries. Foreign players have been coming en masse to France, Germany or Italy. Yet these countries won the 1998, 2002 and 2006 World Cup respectively (Germany also won the European Cup in 1996, and France in 2000).
Some people argued that foreign players have limited the chance of English players to play or be recruited by top teams. That is simply because English players are too expensive, given their (average) quality. To judge the quality of English players, just look at how many Englishmen play in the continent at the top leagues. Currently, none. At its peak, four (Owen, Beckham and Woodgate in Madrid, Hargreaves in Bayern Muenchen; altogether, only them plus Gascoigne and Ince in the 1990s who have ever played abroad).
Italy can have a stronger team because their best players can still outcompete foreigners in Serie A. The French League, on the other hand, is less competitive than the EPL, Serie A or La Liga. There are a lot of foreigners, mainly from Africa, in the French League. But the best of French players are good enough to be the best players in England, Italy or Spain.
In short, the Englishmen can not blame globalization for their crappy performance. Globalization brings competition. It exposes the country's weaknesses that come out because of domestic problems.
Update: I forgot to mention David Platt and Steve McManaman as the other English players who have played in the top European Leagues in the 1990s. Also, Kevin Keegan did it in the early 1980s.