There is an issue across much wider British music scene that people automatically sing with an American accent. They'll speak with whatever their natural accent is, but when singing the vowel sounds come out somewhat american. I've caught myself doing it. Perhaps it's the constant exposure to American accented music with little local to counter it. Perhaps it's an easy, lazy way of enuncuating?
As far as Starlight is concerned - the original cast, Rusty, Poppa and Electra were all played by Americans so used their natural accents. By the "new" recording Dinah had been firmly established as an American character, and Pearl was played by an American. Greaseball really does need to have an American accent regardless, and Rusty? Who knows. Does John Partridge's Electra have an American accent? Personally I dislike the "new" recording enough that I barely listen to it.
In live UK performances Rusty normally has some level of American accent, un-needed. Pearl normally sounds English. Dinah forces a southern US accent to comic effect, Greaseball needs to sound American. Electra I'd say usually does not... then the other characters can use regional accents as part of their character development, Flat-top in particular using it to comic effect.
All US productions of the show have, as is common in their culture, made particular emphasis on the American connection. Here's my favourite, nonsensical photo - who IS the American contender, afterall?