For what it's worth, I strongly believe our ability to catch the targeted accent (British, Am, etc) has to do with the quality of our earing.
If you have got a good musical ear, then you sing in tune.
If you hear well, then you can control the sounds you produce.
Some of us are naturally good at music, others need to work more, but I believe singing helps us all.
Therefore, my personal advise would be to take music lessons, in particular singing lessons.