Germany certainly had their dark moments as well. Just at big tournaments, one can think of the ugliness of the Euro 2000 group stage which ended without a single win and a 3-0 demolition at the hands of a reserve Portugal in the final group game. The anemic 0-0 draw vs Latvia in 2004 in the group stage. In between there were little humiliations like the 1-5 in Romania in 2004, a 0-2 vs a then terrible Hungary in the same year, draws against Iceland and Lithuania in 2003 in qualifying, a defeat at Wales in 2002, two (very lucky) draws with Finland in 2001, two losses vs the U.S. in 1999, a 2-1 win vs Malta in 1998 which essentially led to Berti Vogts' firing in spite of being a win.
Point being that in like 1998-2004 it would have been a fair thing to say Germany doesn't have the talent to play with the big boys and it was indeed said. But in 2004 the Lahm, Schweinsteiger, Podolski generation emerged and it wasn't more than a handful years later the rest of the World Cup winning core emerged.
There would be no natural reason why England couldn't somewhat replicate that if you consider the quantity of youth players England can produce which is at least on par with the likes of Italy and France and well beyond the Netherlands, Belgium, Portugal etc.
Of course, they would need to make major changes to realize that potential and really that's the issue. People get angry at the England team but fast forward a week and it's all about United and Liverpool, Chelsea and Arsenal. The sort of inquiries that should be held aren't held because at the end of the day business is good and the national team isn't needed to help with that. The national team simply doesn't have the same priority that it has in many other countries.