Simple answer is after Pep arrived.
I still recall the murmur around the ground in the first league game at home to Sunderland where the centrebacks pulled wide for goalkicks. Nobody did that. You'd occasionally get one player coming deep, but even then it was pretty much just the fullback launching it instead of the keeper launching it.
City played fantastic football under Mancini.well before Pep arrived obviously.2nd season Mancini ,Silva,Yaya and Sergi couldn't play hoofball if they tried.
The Ipswich Town Side of late 70s and early 80s played a fluid passing game which destroyed many a team on a great Portman rd pitch,most noticeably when they trounced utd 6-3 at Portman rd with their keeper Bailey saving 3 pens. Could have been 9.A great game of football that.
People easily forget about Norwich City playing great attacking football ,again,well before Pep turned up on these shores.Mark Bowen Robert Fleck at.. can't remember the years tho...other players whose names i cant recall...getting old..short sharp passing moves with great movement off the ball..
.i can remember utd going Carrow Road one Sunday pm, live on sky,fergie,as manager, showing great tactical skill,put Paul ince as sweeper...result utd 1 down inside 5 mins.! Ince moved back into midfield...that's how feared Norwich were at Carrow Road at the time...Games between Norwich under Clive Walker were often a culture clash of great passing football,and hit it down the wings and chase from utd,iirc.
Southampton under Lawrie Mcmenamy with Keegan, Ball, Steve Williams Ivan golac etc played great football.late 70s.
West ham under John Lyalll ...Trevor ,Brooking and Alan Devonshire were great to watch,esp at home.
In my opinion,lots of diff teams played good passing football in this country,but as the OP hints ,an awful lot more played kick and rush.
It was Arsenal under Wenger, and not Swansea who broke the mould consistently and successfully ,imo