"The vulgar Americans speak much better than the vulgar in Great
Britain for a very obvious reason viz. that being much more unsettled,
and moving frequently from place to place, they are not so liable to
local peculiarities either in accent or phraseology. There is a
greater difference in dialect between one county and another in
Britain than there is between one state and another in America."
(dated 1781, quoted by Melvin Bragg in 'The Adventure of English')

The vulgar British are much more mobile and unsettled now than they
were then, and there's been a lot of dialect levelling and erosion of
accent differences. But in language history there's divergence as well
as convergence, and Kevin Watson, in 'Phonological resistance and
innovation in the North-West of England' (English Today 86, April
2006) describes how Liverpool English is resisting the T-glottalling
which is generally on the increase in England, and how other,
regionally distinctive, realisations of /t/ are appearing in an
increasing variety of phonetic contexts in this accent.