The usual position under public international law is that obligations under a treaty persist even after a revolution^1
In this case, neither the PRC nor the UK made the argument that the Qing dynasty was an entirely separate entity to the PRC. it was actually the UK that insisted that the relevant treaties still applied - since their presence in Hong Kong relied on those treaties. The PRC relied on a doctrine of ''unequal treaties'', essentially that the relevant treaties were unfair, that they were negotiated between parties of substantially unequal power, and could be abrogated at any time.^2
Revolutions, Treaties, and State Succession The Yale Law Journal Vol. 76, No. 8 (Jul., 1967), pp. 1669-1687
Roda Mushkat: One Country, Two International Legal Personalities: The Case of Hong Kong, Hong Kong University Press, 1997