He's always spoken like that, with the sporadic Yankish popping up - It's the accent of a typical Brit who spends a lot of time in America, hence the slight twang creeping in.
Although annoying, it's actually well-suited to the characters he plays, ie Brits in America.
While not a fan personally, I admire how Statham has basically parallelled Steven Seagal's film career, but without becoming a complete bell-end about it.