I found a 1975 study from Sherman about this (backup link).
Those stress changes are really old and affect a lot of noun/verb pairs (more than just the -ate ones). Most variation was attested in the XVIII century, but at least one ("accent") already showed some variation back in 1634. (Check page 57 (PDF page 15) for a list.)
And in some cases you see three competing stress patterns for the same pair - both oxytone, both paroxytone, and diatone (paroxytone noun, oxytone verb); e.g. "bombard", "cement" and "outcast".
So, no, the presence of this variation in the UK is not due to USA influence. It was born there, and then spread to USA.
As for an explanation on why this happens: I don't know. But if I had to guess, it's a "conflict" between English "preferring" the stress in the first syllable, and "trying" to keep noun/verb pairs distinct.