As far as I know, East Asian way of teaching is nothing different from British way of teaching. However, more than a half of EA students go to cram schools in the evening and they get supplemental trainings + massive amount of homework every week. If kids aren't serious, the cram schools call parents, and warn parents they can kick their kids out. Many parents start to send kids to cram schools when kids get 10-ish. All those efforts are made for very competitive university entrance exams.
My opinion is perhaps proven by the PISA score by Asian Americans kids.
Although they have even crappier secondary education than UK, their average score was exactly same as EA countries.
Overall PISA rankings, including America by raceOECD average 496 501 494 497
Shanghai-China 570 580 613 587
Singapore 542 551 573 556
Hong Kong-China 545 555 561 554
Asian Americans 550 546 549 548Korea, Republic of 536 538 554 542
Japan 538 547 536 540
Chinese Taipei 523 523 560 535
Finland 524 545 519 529
This mystery can be easily solved if we know many Asian kids in USA also use some sort of supplemental schools in the evening.
So if you want to introduce EA solution, it's very simple. A) All public universities (or at least Russell Group unis) are legally forced to require candidates to take an A-level in Further Mathematics, even for art and humanity studies. B) you open a cram school business in the UK
University entrance exams are the fundamental indicators of secondary education. If those exams become more difficult, students study harder. There should be a correlation between the introduction of curriculum 2000 and the fall of UK on PISA.
TBH, I personally don't think it's necessary to copy EA education system. Not all students need advance math for their studies. I know many students studying Social Science or Art and Humanities and they are highly intellectual and logical without math knowledge.
But current A levels may be better to be reviewed once, because of grade inflation.