w00t! I win! Southern Electric lose! They suck!
They sent me bills for the brief time they'd stolen me away from Scottish power, but I phoned 'em up and shouted at them (in a very quiet and reasoned way) and they've canceled the bill. Result!
Now I just have to give SP the meter readings from the start of the bills and life can go on. Although I suspect I need to poke SP to sort me out the right sort of bill first. But I'm getting there - it's only take 4 months to sort out changing my supplier.