The first caveat is that no country in the world provides 100% accurate figures, nor even can they. The UK is no exception -- and, incidentally, no we haven't over-reported deaths, with the possible exception of the period around August last year when the count was "deaths among all those who had a positive test no matter how long ago that test was", which obviously would overcount more and more over time.
The second question is what the figure even being officially reported is. In most countries, the official count is based on deaths among confirmed positive cases. If the epidemic in India is growing out of control faster than critical patients can be tested, then many who die of Covid might be missed from the official figures by virtue of being untested. This wouldn't be a conspiracy or a cover-up, but incompetence at most. Equally, if the system is overwhelmed then it becomes a lot harder for officials to keep track of the data anyway.
Regardless, this is all terrifying, but right now the priority is surely to provide help to India as much as is possible.