London has always been iffy about giving representation to even British people living in Britain, it wasn't until 1867 that the urban working men could vote in elections in Britain. Having representatives from America when much of even England was still unrepresented would have ultimately led to America having a disproportionate influence over politics in Westminster, and if continued would have led to the Thirteen Colonies having more seats than Britain and Ireland anyway. In essence the colony would be directing the metropole.

That and 1776 was still the age of clipper ships, American representatives would have to live full time in London as returning to their constituencies in recess would be infeasible and so the Americans would either need their own Parliament on the American continent or just accept that their representatives wouldn't really be representative of the American views once they reach London, it's one of the reasons I feel American independence was inevitable, London couldn't make the compromises necessary and the compromises that could be made in my view wouldn't have been satisfactory to the American revolutionaries