Its a perception thing which is deeply rooted in the history of the game. We codified the game and were so sure of our preeminence that we never bothered to develop and didn't even bother to join FIFA. Tactics? Tactics were for Johnny Foreigner. He was too weak and too scared to play the game properly so he had to use
tactics, which was tantamount to cheating. This view continued into the 1930s and 40s and English managers who wanted to employ tactics were laughed at. But some of them went abroad and learnt from the foreigners who had taken our game and improved it. People like Arthur Rowe came back in the 1950s and won the title with Spurs using the 'push and run' approach. Slightly later Vic Buckingham did the same thing. They'd learnt from the so called Danubian School which, through the Magical Magyars of 1953, visited upon England their first major trouncing by a non-British side. Ironically, the Danubian School was influenced by other British coaches who had gone abroad taking with them ideas spawned by the notion of passing the football, first carried out by Queens Park of Glasgow. As
@FellTop says, many foreign coaches, particularly Guardiola and Mourinho were influenced by people like Bobby Robson but its possible to trace a line back from Guardiola, through Robson, through Buckingham, through the Danubian School, right back to Queens Park.
However, despite this, I am firmly of the opinion that English coaches are still looked on with scorn. We now want to embrace innovation and and a highly tactical, technical approach but firmly believe only foreigners can do it. Just look at how many of even our fans respond to Lee Johnson when he talks about the technicalities of the game. "He thinks he's too clever", "he talks in jargon" etc. If his name was Leo Giovannifils, everyone would lap it up.
So, in my opinion we're all stuck in the past. There are lots of great English/British coaches but fans/owners think a foreigner is better. We all despise David Moyes but I know for a fact that amongst his colleagues, his reputation is second to none. English managers are just as good as anyone else but we don't expect them to be and they're not fashionable.