Boris Johnson is to inject £1.8bn into the NHS as part of his pledge to upgrade 20 hospitals across the country, it has emerged.

The new prime minister has used a boost in health funding as part of an attempt to build a domestic agenda beyond Brexit, with his team well aware that they could be forced into an election this year. But experts have already warned that the fund may not be enough even to cover the upgrades Johnson has already promised.

Full details of the plan are set to be revealed on Monday, but it is understood the new funds will be directed straight to the front line for new beds and updated equipment. It is also set to include upgrades to wards and some building repairs.

The money is set to be made available immediately, though Downing St has not revealed where it will come from. Johnson has already made clear he is willing to spend more money on public services, using the so-called “fiscal headroom” created by the previous government’s spending plan. The headroom was supposed to help the economy in the event of a no-deal Brexit.

A source said: “The prime minister has been clear since day one that the NHS is a top priority. This money will be felt by frontline services, by the doctors and nurses whose hard work is invaluable, and by the patients they care for.”

The Vote Leave campaign controversially argued that funds sent to the EU would be used to fund the NHS instead. Dominic Cummings, the Vote Leave strategy chief now overseeing Johnson’s Downing St plans, said such a pledge should have been one of the government’s first moves after the Brexit vote.

Researchers at the Nuffield Trust thinktank have suggested that Johnson’s promise to upgrade 20 hospitals would cost at least £3.2bn, based on an assessment of hospitals two years ago.

“Based on the conservative £160m cost estimate per trust, the total cost for upgrading all NHS services would be around £33bn,” tweeted Sally Gainsbury, a senior policy analyst at the trust. “That wouldn’t all need to happen at once – it takes time to build a new hospital wing after all. There have been calls to double the NHS budget for NHS investment – including from the NHS’s own regulator NHS Improvement. That would take investment to around £14bn next year.”