Unfortunately this is the reality, but it's worst case scenario stuff. However, I'd have thought the immigration officer would have every reason to raise an eyebrow over the fact you book a flight from India to the US on a combination that requires an overnight stay in London when many other options exist.

We have some major issues in the UK with historically lax enforcement of immigration policies. The current government are trying to get a grip on this - they have to as its costing them votes!