When I presented British /ӕ/ sound to three Korean English-familiar persons online - they are doing answering English-related questions activities [case 1; case 2], and asked what sound it’s like /ӕ/ or /ɑ/, astonishingly all three of them without hesitation checked out /ɑ/. That shows how difficult it is to differentiate the two sounds for Koreans.
I can perceive both British and American /ӕ/ are made at the front. But the former sound is far more similar to Korean’s “ㅏ” sound. That’s why the Koreans all hear /ɑ/. And this definitely shows, I wonder, that there’s some difference between British and American /ӕ/. Would you let me know the difference?