What about a kind of Clive-less World scenario, only where the French don't totally overtake the sub-continent instead? It would be jimmying the rules a bit, but you could have a scenario where Britain only controls the east coast and Bengal for a much lower population. If you preserve the eastern Princely States under company rule, too, and make them autonomous units without voting rights you could make it so that only those Indian subjects under the direct rule of the Crown have representation, meaning you might just be able to keep a situation where the UK is not outvoted by India but has a slightly larger population.
Clutching at straws, I know, but it's an idea.