England's WC/continental cup history is poor compared to Argentina, Brazil, France, Italy and Germany. And it's similar to/slightly better than Holland and Spain.
But it's better than Croatia or the Czechs.
From 1990 onwards, England reached the WC semis once and two Q-Fs.
The Czechs played it once (2006) and were eliminated in the group stage (and the Czechoslovak reached the Round of 16 in 1990 IIRC).
The Croats played 3 WCs and reached the semis once and were eliminated twice in the group stage.
In the EC (also 1990s onwards), the Czechs (semis once, final once) did better than England (semis once, Q-Fs) while the Croats reached the Q-Fs once and were eliminated once in the group stage.
Of course, Croatia and the Czechs nowadays seem to have better national teams than England, but neither of them is bigger than England.
The fact England have played most WCs (and won it once) and did reasonably well in most of them (they were only eliminated twice in the group stage) makes them much bigger than Croatia or the Czechs.
In order to be big, you have to do consistently well for several decades, which isn't something the Czechs or the Croats have done (yet, at least).
Obs: I never imagined I would defend the English nat'l team!