The historic administration of Hong Kong was centralised on a small number of senior administrators. The Government in Hong Kong consisted of the Governor, the chief secretary who was in charge of the civil service, a financial secretary, a secretary of state for home affairs, an attorney general and a commander of British armed forces stationed in the colony, all appointed from London. Each was an official advisor and formed an Executive council with nine further Hong Kong citizens chosen by the governor, with each person acting in an advisory role. The annual budget and taxation policy was decided on by the financial secretary. Many decisions made by the Executive Council were then legally ratified by the Legislative Council. This latter council was wholly appointed by the governor and consisted of executive members of the administration, department members of the civil service and ‘unofficial members’. The legislative council passed laws, assigned funding and raised questions on behalf of Hong Kong citizens; however no motion could be debated unless first proposed by the governor.

After the signing of the Sino-British Declaration of 1984, dealing with the future of Hong Kong, attempts were made to democratise the system by bringing in elections for the Legislative Council. Therefore 24 of 57 of its members won their seats by election in October 1985. Prior to this, the only partially elected body had been the Urban Council that was responsible for overseeing public health, recreation, licensing, culture and amenities. Regarding the latter part of your question, during sovereignty negotiations, British PM Margaret Thatcher impressed on Chinese Communist Party Chairman Deng Xiaoping that the UK did not receive any taxation revenue from Hong Kong.

In Summary: The UK government appointed the governor and most important administrators. The budget was decided by a locally based but UK appointed financial secretary and Hong Kong taxation (At least in the 80s – the time period I have knowledge of) did not fill the coffers of the UK treasury.

Sources: W. Zhang, Hong Kong: The Pearl Made of British Mastery and Chinese Docile-diligence (New York, 2006)

C.Mark, “To ‘educate’ Deng Xiaoping in capitalism: Thatcher’s visit to China and the future of Hong Kong in 1982” Cold War History (2015) pp. 1-20

EDIT: Formatting