As long as there remains the scent of faith in the hearts of our heroes, so long shall the sword of Hindustan flash before the throne of London- Padishah Bahadur Shah II
This is just a very vague idea.
Can we get Britain so embroiled in other wars in 1857 that the Indian Mutiny actually succeeds in defeating the Company forces in India (at least in the short term)? Lets say that, e.g. the Sikhs throw in with the mutineers in the interests of reviving an independent Punjab.
Let's say an earlier Crimean War combined with higher tensions with Civil War America leaves Britain overstretched. The mutineers drive the Company from North India and proclaim Bahadur Shah, the Mughal Emperor as their titular overlord, ushering in an era of warlordism in North India.