About 30 people assembled outside the building in the city's Admiralty district, some waving the yellow umbrellas that are the symbol of pro-democracy occupations that have blocked roads in key districts for nearly two months.
"The UK is obligated to solve the problem... Britain bears half of the responsibility as it signed the joint declaration," 21-year-old student organiser Daniel Ma told reporters.
Britain and China are signatories of the 1984 Sino-British Joint Declaration, an agreement that enshrines rights and freedoms unavailable on the mainland and asserts "the current social and economic systems in Hong Kong will remain unchanged" for the 50 years following the 1997 handover.
"Democracy should be based on Hongkongers' will," Ma said. "It was a promise that for 50 years we have would have a high level of autonomy."
"The UK cannot stay silent. If you are silent you are part of the same evil," he added.
After handing over a petition to consulate officials, Ma said the group would camp outside until Britain officially condemns China for breaching the declaration.
Housed in an unremarkable building, the British consulate stands in great contrast to the former colonial governor's mansion, which is now inhabited by embattled city leader Leung Chun-Ying. A British royal coat of arms and images of Union flags offer the only clue to its purpose.
British Prime Minister David Cameron has said he is "deeply concerned" about tensions in the city after police used tear gas on protesters at the end of September.
But he has yet to go as far as US President Barack Obama, who said the United States would "encourage people's right to express themselves."
"We consider that the rights and freedoms enshrined in the Joint Declaration and Basic Law continue to be upheld, and that it is these rights and freedoms that underpin Hong Kong's success. Our commitment to ensuring the faithful implementation of the Joint Declaration is as strong as ever," she said in a statement.
Hong Kong residents enjoy rights not seen on the mainland, including freedom of expression and assembly.
