The reason we're so good at American accents is because we hear them one hell of a lot. About 50% of what's shown on TV is American. How much American TV is British?
We don't accept the term 'British accent,' because there is no accent that sounds Welsh, Scottish and English at the same time.
Denzel Washington carried it off in this film because he didn't attempt a 'British' accent, he spent some time in the East End and spoke with an East London accent.
Dick Van Dyke spoke with an accent that you only hear in Disney films. Nobody over here uses the term 'guvnor,' nor pronounces lovely 'luvverly.'
The 'ugh' sound predominates over here, and Americans are often caught out using the words 'pentagon' and 'python.' We say 'Pen tugh gughn' and 'py thughn.'