It is certainly possible (but very in actual history, unlikely; see below) to do that, at least the part where someone in London and/or Delhi draws lines on a map. But the overwhelming odds are that it would end as a major clusterfuck. As in, humanitarian crisis on a WWII scale or worse, with warfare all over the subcontinent (most of it low-level), tens of millions refugees everywhere, messed up and contested borders, and probably internal violence and likely military rule in many of the resulting states as a consequence. In short bloodbath and a constant mess afterwards. While India is hardly paradise IOTL, trying to carve semi-homogenous nation-states out of it in 1947 would arguably make it MUCH worse. A peaceful division is hardly workable: hell, even the division of the federal states within the Indian Union IOTL has led to violence. Guess what happens if the corresponding conflicting claims are backed by sovereign states with actual armies and, in all likelyhood, a nationalistic frenzy. Think OTL's India/Pakistan is bad? That would be like ten of those.
Not that it had any significant chance to happen anyway in OTL conditions. Calls for such a thing, AFAIK, were rare and nobody whose opinion really mattered ever considered it seriously.