Boris Johnson will try to use the Queen’s speech to refocus attention away from Brexit and on to the NHS, the government has confirmed.

The prime minister intends to put the health service at the centre of the legislative programme, according to the chief secretary to the Treasury, Rishi Sunak.

Speaking to BBC Breakfast he said: “The heart of this Queen’s speech today will be our record funding settlement for the NHS: £34bn over the next five years.”

He added: “The prime minister said we want to be the people’s government. Of course we want to get on and start getting Brexit delivered ... but then there are all the other priorities that we talked about and the heart of that is the NHS.”

Sunak also confirmed plans to put extra funding into social care, but he appeared to water down Johnson’s pre-election pledge to guarantee that no one needing care would be forced to sell their home to pay for it. Sunak relegated this promise to a “belief” and prepared the ground for blaming opposition parties if it was not met.

He said: “We will invest an extra £1bn to stabilise the system from the immediate pressures. Secondly we will work urgently to find a cross-party consensus on this issue and thirdly underpinning that solution will be our belief that no one needs to sell their home for care.”

He added: “Unless there is a cross-party consensus we won’t have the security and certainty that the problem is solved.”

The Queen’s speech will also include proposed legislation to abolish hospital car parking charges for “those in greatest need” – likely to include disabled people, parents of sick children staying overnight, and staff working night shifts. The high street is reported to be set for a boost, with a cut in business rates from April.

Johnson said he wanted to use the second Queen’s speech in 10 weeks to put forward an agenda also centred on law and order, infrastructure and education.

Sunak said: “We are also focused on making sure our communities are safe, with more police and tougher sentencing and we are interested in level-up opportunity across the United Kingdom with investments in infrastructure and education. So taken together I think it is an exciting and inclusive agenda.”

The speech will be more low-key than the last one in October, with cars used instead of carriages and the monarch wearing a hat instead of a crown.

It will commit to increasing levels of funding per pupil in schools. New legislation would also seek to ensure terrorists spend longer behind bars and make it easier for police to stop and search known knife carriers, Downing Street said.

Brexit legislation will be prominent, with the speech including proposals to implement the UK’s future relationship with the EU, which is due to be agreed by the end of December 2020.

The legislative measures will also include proposals to “stop vexatious claims” against members of the armed forces.

The shadow health secretary, Jonathan Ashworth, said: “The re-election of this government passes them the great responsibility of fixing the crisis in the NHS, which 10 years of their underfunding has created.

“We will study the legislation they are putting forward, but the commitments from their election manifesto fall far short of what is needed to end record waiting times and staff shortages.

“If the Conservatives’ plans to put funding increases into law is to be anything other than an empty gimmick, we would urge them to pledge the extra £6bn a year which experts say is needed to start to make up the cuts they’ve imposed for a decade, and to put the necessary funding into public health and social care.

“This government will be judged on its handling of the NHS and its ability to put right their disastrous handling of our country’s most important institution over the past decade.”