I don't think Chelsea can be said to have played "the English way" against either Barca or Bayern. As carrabuh says, they simply did what gave them the best (or only) chance of winning -- much as teams often do when they go to the Emirates. They defend in numbers and hope to get a goal on a quick counter-attack when they have frustrated the more positive team into pushing too many players forward. The "English" way is more a case of wide-open, we attack then you attack, fast and furious ding-dong. We've seen less and less of this with the arrival of foreign managers, but it still colours the mental approach of our teams to a certain extent and is certainly what the majority of fans hanker after: fast, raw and physical.
With Barca/Spain having very much dominated for a few years now, there are signs that things are moving beyond them -- as always happens. People work out how to play against that particular style -- as Mourinho has sussed out this year at Real. However, there is one factor that hasn't changed enough in our game, and that is technique. Virtually every non-British team or country you watch can outdo us in technique -- even simple passing accuracy. As redruth and other have been saying, we have been behind in that respect for many years, and it will take another generation before it is going to significantly improve -- if indeed it ever does!
[EDIT] By "us" of course I mean English players, whether for team or country. The foreign players in the Premier League generally do have far better technique, and in my opinion, generally have better understanding of the game. Too many of our modern players seem to wait to be told from the touchline what they should be doing. Where have our Bobby Moores gone?