Thirty years after British and Chinese leaders signed an agreement returning Hong Kong to Chinese rule, the U.K.’s parliament is launching an inquiry to examine what role the former colonial power should play in Hong Kong’s social and political development.

Pressure has mounted in recent months, both domestically and abroad, for the U.K. to take a more aggressive position as Hong Kong’s fight for universal suffrage in its 2017 elections heats up. While Hong Kong’s relations with mainland China are governed under the “one country,...