A senior government minister has raised further questions over Britain’s relationship with the European convention on human rights (ECHR) as Boris Johnson scrambles to push through tougher sentencing for terrorists.

Legal experts have suggested the government’s intended plan to extend the time terrorists serve in prison could be in breach of the ECHR, to which Britain has been signed up for decades.

Asked what he made of the warnings, Matt Hancock said he had heard the arguments from those against the changes but that they should go ahead.

The health and social care secretary said: “What about our human rights? What about the human rights of people to be able to walk freely around the streets of London?”

Following the Streatham terror attack on Sunday, and deaths of two people at London Bridge last November, the government wants to table emergency legislation to ban the automatic release of prisoners halfway through their sentences. Instead, they want to increase the minimum time served to two-thirds.

Lawyers think prisoners could appeal against the proposed changes, which are due to be tabled by the end of the week, as the ECHR contains guidelines on retrospective reforms to prison sentences.

Asked again about the protests from human rights advocates who say the changes would be in breach of the ECHR, Hancock told Sky News: “Well, it is in favour of the safety of the public. Sometimes people are released before the end of their sentences. It’s not about extending sentences. It’s about when people are released relative to the end of their sentences.”

He added: “Often in government you get a point where you have to balance the rights of different people and in this case it’s weighing up the rights of an individual whose committed terrorist offences and his right to leave prison early against the rights of people to walk around Streatham or anywhere in our country free from the threat of terrorism.

“So I hear the arguments that some people are making that actually we shouldn’t make these changes but I think that I feel very strongly that we should and so would the vast majority of the British public I would imagine.”

The ECHR is a separate institution to the EU and Britain remains a member and bound by its rules. It can derogate – in effect take a temporary break from it – in circumstances of emergency, war or “threat to life of the nation” under article 15.

The government has so far not suggested how it could bring in the new terror sentencing laws and abide by the ECHR, or whether it will ask to derogate.

The prime minister’s official spokesman said on Tuesday: “We are going to ensure that we will bring forward the necessary legislation to protect the public because that is the right thing to do.”

Asked again if the government would deviate from ECHR rulings to bring in the fast-tracked laws, he said: “As the justice secretary said, we believe that we can bring forward this legislation and we are committed to doing so.”

On whether the government considers the current situation an emergency, he said: “That’s not something we have set out.”

The UK derogated from article 5 of the ECHR, the right to liberty and security, during the Troubles in Northern Ireland.