Not sure if the extent of foreign players is the thing to blame. Barcelona, Real Madrid and Bayern München are rich, powerful clubs with a lot of foreign players. Yet, Barça & Real were the basis of the Spanish national team that dominated world football in late 2000s to early 2010s, and Bayern was the basis for the German domination in 2014. If a player progresses enough, he'll get the call. I'd even argue that English players are favored over foreigners in the Premier League, which results in an overvaluation, which then results in English players in general overrating themselves.
The second part of your post (lack of players and coaches that go abroad) is the actual problem I think. English football, as stated by Brigs, has a sense of entitlement because they created the sport. They've had this "We created it, we know it the best" mindset for decades. It results in a very conservative approach to football strategies that are ever-evolving and English football gets left behind as a result.
In light of the recent passing of Johan Cruyff, it's worth remembering that the foundation for Barcelona and Spain's domination in world football prior to the last World Cup lies in Johan Cruyff coming over to Barcelona and establishing the Total Football philosophy there. Barcelona, and then the national team adopted a style that originated in the Netherlands, added their own twist to it and dominated the game. The introduction of the likes of Jürgen Klopp and Josep Guardiola as coaches into the league might spark something.