The only way for India to seek China's support for its accession to the United Nations Security Council is for India to replace the UK's membership of the UNSC. Legally speaking, when Britain became a member of the UNSC, India remained a British colony, that means India of course could represent the British's position in UNSC, not necessarily forever the small islands of Europe.
Moreover, in reality, UK has weakened to the point where even Scotland is about to become independent, and its foreign policy completely replicates that of the United States, without any independence. No one believes that it still deserves the status of an UNSC member. The global South, China, Russia, and France will definitely support such an arrangement, and India only needs to lobby the United States. Never mind UK's opinions, they will listen to Americans anyway.
