The UK should allow complete freedom of movement for medics from around the world, the Tory leadership hopeful Matt Hancock will pledge on Monday.

The health secretary, who is one of main contenders from the party’s centre-left in the 13-strong race to be the next prime minister, will promise to lift all immigration restrictions for qualified doctors and nurses of any nationality who have secured a job in the NHS.

Hancock will use a speech on the future of NHS staffing to outline his plan if he becomes the next prime minister. In the speech, seen by the Guardian, he will say: “Our NHS could not provide its world-class service to patients without the hardworking doctors and nurses from other nations. That’s why I believe, after Brexit, we need to see the free movement of medics – doctors and nurses – from all around the world.”

Hancock will say the only limitations should be the right qualification, a job offer and an ability to speak English. “Wherever you’re from, if you’re qualified, speak English and have a job offer, I want you to have an unrestricted right to work for our NHS and live in our country. We have the best health service in the world - and if I become prime minister, I will make sure it has access to the very best talent in the world.”

Last summer the government announced it would exclude foreign medics from its cap on skilled migration after an outcry from NHS bosses about the numbers being turned away at a time of critical short staffing.

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The FT reported at the time that 2,360 visa applications by doctors from outside the European Economic Area had been refused in a five-month period, despite there being vacancies for almost 10,000 doctor posts alone in NHS England.

Medics are now exempt from the cap on tier 2 visas, used by employers to bring skilled workers to the UK from outside the EU. However, the home secretary, Sajid Javid, told the Migration Advisory Committee (MAC) when it was exploring the government’s post-Brexit immigration policy that the decision to relax the rules was temporary.

Hancock has positioned himself as the candidate most likely to win a significant bloc of votes from party moderates, though he has suggested that a no-deal Brexit is unrealistic given the numbers opposing it in parliament – a position that has alienated him from the party’s right.

“No deal is not an available choice to the next prime minister, whether they like it or not,” he wrote in a letter to Tory colleagues on Sunday setting out steps he would take to renegotiate the political declaration, including adding a time limit on the Irish backstop and setting up an Irish border council to agree long-term arrangements.

Javid, who is also running for leader, will set out his policy stall on Monday with a plan for a £100bn infrastructure fund for regeneration outside London and the south-east, including examining plans for high-speed rail networks between northern English cities.

Javid would be one of the first leadership contenders to admit he would fund ambitious plans by borrowing to invest. His proposal suggests a new fund in addition to the government’s existing commitments, which would be an “arms-length” body and would sit outside London with an independent board making funding decisions.