The British prime minister Theresa May has stepped into the growing crisis over China’s controversial plan to change the extradition law for Hong Kong citizens, by saying it was vital this did not breach the joint British-Chinese declaration, agreed at the time of the city’s return to China in 1997.

In her first comments since protests started in the semi-autonomous city last week, the British prime minister said she was deeply concerned and the UK had a special responsibility to speak out in favour of freedoms in the former British colony.

“We are concerned about [the] potential effects of these proposals particularly obviously given the large number of British citizens there are in Hong Kong,” May told parliament.

“But it is vital that those extradition arrangements in Hong Kong are in line with the rights and freedoms that were set down in the Sino-British joint declaration.”

The foreign secretary, Jeremy Hunt, responded to growing calls to intervene by urging China to preserve a high level of autonomy in Hong Kong and engage in meaningful dialogue.

With the UK possessing scant legal leverage over Hong Kong’s future, Hunt opted instead to urge China to recognise it was in its own interests to show restraint, in order to preserve its international reputation.

“The ongoing protests in Hong Kong are a clear sign of significant public concern about the proposed changes to extradition laws. I call on all sides to remain calm and peaceful,” he said in a statement.

Hunt also urged the Hong Kong authorities “to listen to the concerns of its people and its friends in the international community, and to pause and reflect on these controversial measures. It is essential that the authorities engage in meaningful dialogue and take steps to preserve Hong Kong’s rights and freedoms and high degree of autonomy, which underpin its international reputation.”

He continued: “Upholding the principle of ‘one country, two systems’, as set out in the legally binding Sino-British joint declaration, is vital to Hong Kong’s future success.”

Hunt had already issued a joint statement with the Canadian government urging China to give the Hong Kong legislative council time to come up with alternative extradition proposals that maintained business confidence. There are fears the legislation could be pushed through within a week.

Britain’s minister for Asia, Mark Field, told MPs on Monday that recent concessions on the proposed law fell short of protecting the city’s autonomy and judicial independence.

“There are widespread concerns that fear of extradition to China might have a chilling effect on Hong Kong’s rights and freedoms and result in increased self-censorship … Hong Kong must enjoy the full measure of its high degree of autonomy and rule of law as set out in the joint declaration and enshrined in the basic law,” he said.

“Many fear above all that Hong Kong nationals and residents risk being pulled into China’s legal system, which can involve lengthy pre-trial detentions, televised confessions and an absence of many of the judicial safeguards that we see in Hong Kong and in the UK.”

Hinting that the UK could declare a breach in the joint declaration, he said the extradition bill came close to representing a breach, not just of the spirit but of the text.

The last British governor of Hong Kong, Chris Patten, has said the extradition bill’s provisions are “a terrible blow … against the rule of law, against Hong Kong’s stability and security, against Hong Kong’s position as a great international trading hub”.