Manchu are Chinese. British are not Indian. You can not just inherit everything from British. Even if you can, why can't Pakistan? Why not other countries?
In addition, just like Bhutan, Ladakh was a vassal state of China (or protectorate country or tributary country or whatever the translation). Since it is not a country anymore, we do have right to claim it.
China wanted to set up the border dispute with your country, but you refused. And you wanted to invade China, but you overestimated yourselves. So you stabbed China first, better blame yourselves for today's situation.