The British state would have had a lot more money, as they wouldn't have been bailing out the corrupt East India Company again and again.
There would also be fewer "nabobs": unscrupulous military men that went out to India, ruled like tyrants for a few years, channeling money into their own pockets, and then came back home and bought seats in parliament, with very right-wing reactionary views.
A lot of those "nabobs" were also the men willing to assimilate to Indian cultural traditions when they went out East; something that occurred much more under Company rule than under that of the Crown. Important leaders were also built up with Indian capital; I believe Pitt was one of those.
Britain without India alters the global balance of power and allows the creation of an Indian one. While I still think formal unity would continue on in India it might start to resemble Ottoman Tunisia, Algeria and Egypt in practice. Many of the Indian states for reasons of distance, population, basic industry, etc. might be able to forge their own spheres of influence. Tipu's Mysore was one that was very ambitious in scope, for one. Britain keeping some exclaves in India like Bombay or Calcutta might certainly change the flavour of those cities and create the beginnings of a proper Anglo-Indian cultural mix that still might find itself influential in Britain.