Lothar Matthäus is an obvious one, I think...quite surprised he hasn't been mentioned already. English football has hosted a ton of highly influential dynamos in midfield positions through the years — from the likes of Bremner and Souness to Robson and Keane to Vieira and Gerrard — who were all talismanic for their respective teams and were afforded a decent degree of freedom in a somewhat loose structure. And a tour de force performer like Matthäus would be deeply appreciated for his all-encompassing heroics from the center of the pitch. Then again he was awesome in Germany and Italy, so he didn't necessarily need to move to England to improve his profile/credentials.
In fact, a lot of German or Bundesliga based footballers should've/could've played in England because they were stereotypically associated with qualities like physical prowess, grit and efficiency (which are often considered hallmarks for success in the English game). Even someone like Olivier Bierhoff would be a good match when you consider his profile — absolute unit, and an imperious header of the ball...would do well in a kick-and-rush style team alongside a “little guy” second striker from the '90s!
For centerbacks, I'd say former Werder Bremen great Rune Bratseth — 6'4" tall, rock solid in defense, technically accomplished in a sweeper role, and always up for a challenge — essentially an improve version of Sami Hyypiä. And for fullbacks, Javier Zanetti — loyalty is considered a profound virtue and Serie A is the spiritual home of the art of defending, but he just wasted soooo many of his prime years at Internazionale (won only one UEFA Cup and one Coppa Italia title in a decade before Calcipoli and the subsequent arrival of Mourinho).