Britain colonized a lot of nations including India, Pakistan, Bangladesh, South Africa etc. Why would India get exclusive right over others? That's just expending needless energy into a failed venture.
Whether the British colonies are eligible to inherit the 1945-British seat should be judged by the United Nations General Assembly. As long as India can get 75% of the vote, it can pass.
I think former British colonial countries all will support India, because this is not only India's opportunity, but also theirs.
More importantly, other countries will certainly not be willing to add a permanent member, but they may not mind changing a permanent member.
Of course, if India succeeds. The United States, China, Russia and other countries will certainly support other Commonwealth countries to compete for seats. India needs another vote in the UN General Assembly. If China wins, I think you can guess who will get the seat...
But China claims Aksai China and South Tibet.
Why would China give up land?
That's just my guess.