That's what they teach kids in school history in Britain, but the actual fact is that Germany had no way of crossing the channel, especially with the Royal navy fully in the game, the luftwaffe was worn from the campaign in France and Poland as well as mechanically stretched after the first few weeks of the Battle of Britain, tye narrative has been, the raf were struggling and were saved by the change to bombing cities, but they actually had more aircraft available then than they did at the start, no hitlers error was attacking them at all, instead of pausing for a while and trying to negotiate, but Britain had Germany blockaded too.

Lots of ifs and buts