LONDON—British Prime Minister Boris Johnson Tuesday announced tax increases to support the country’s state-funded National Health Service as it struggles to manage a backlog of millions of patients in the wake of the Covid-19 pandemic.

With the announcement, Mr. Johnson is renouncing an election pledge not to raise payroll taxes, a move that sparked criticism from within his own Conservative Party and underscored the pressure the pandemic has put on governments to find funding for social services stretched by Covid-19 and aging populations.

The U.K. government will increase payroll and dividend taxes by 1.25% respectively to raise £12 billion, equivalent to $16.5 billion, a year starting in 2022. The government aims to pump cash into the NHS and, in the longer term, overhaul the country’s social-care system.

“It would be wrong for me to say that we can pay for this recovery without taking the difficult but responsible decisions about how we finance it,” Mr. Johnson told Parliament. “It would be irresponsible to meet the costs from higher borrowing and higher debt.”

‘A global pandemic was in no one’s manifesto,’ British Prime Minister Boris Johnson said Tuesday.

Photo: Toby Melville/PA Wire/Zuma Press

Across the globe, governments are wrestling with how best to fix budget holes left by Covid-19. While the Biden administration pushes for a $3.5 trillion spending plan funded in part by tax increases, most European governments have held off tax increases as their economies emerge from the pandemic. In Europe, “the U.K. does seem to appear to be somewhat of a trailblazer in taking steps to raise taxes,” said Christine Cairns, a personal tax partner at accountancy PwC.

Despite historically low U.K. government borrowing costs, Mr. Johnson said funding the health system with more debt would be irresponsible as it would pass costs onto future generations. Increasing taxes is “not something that I do lightly but a global pandemic was in no one’s manifesto,” he said.

The U.K. suffered the worst downturn among the Group of Seven advanced economies in 2020 and experienced one of the deadliest coronavirus outbreaks in the world. However, with some 80% of the eligible population now vaccinated, social distancing restrictions have been eased and the government is aiming to move on from the pandemic.

The country’s health system remains sorely tested by the public-health crisis. The NHS rode out the pandemic despite years of underfunding, but the flood of Covid-19 patients has left it with 5.5 million people waiting for treatment, a figure the government says could rise to as high as 13 million if extra funds aren’t made available.

The extra funds raised by the new taxes will first go to boosting the NHS’s capacity, with subsequent financing going to overhaul the country’s social-care system.

In raising taxes, Mr. Johnson is denting his Conservative Party’s reputation for low taxation. In March, the U.K. announced plans to raise corporate tax to 25% from 19% from April 2023 and to freeze tax-free allowances on personal income. The government also Tuesday temporarily suspended a pledge to raise state pensions in line with wage growth, which is expected to hit around 8% this year.

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The latest tax increase sparked protests by members of the Conservative Party, who said the burden of funding the overhaul of social care would fall disproportionately on the poor and play into the hands of the opposition Labour Party. 

The national insurance payroll levy is paid by both employers and employees. Labour Party leader Keir Starmer said Tuesday that Mr. Johnson’s tax increases were akin to putting a bandage “on gaping wounds that his party inflicted” and questioned why the taxes weren’t levied more directly on the rich. The government says that the richest 14% will pay around half of the extra tax revenues.

The British Chambers of Commerce, a business lobby, opposed the tax increase, calling it “a drag anchor on jobs growth at an absolutely crucial time.”

Mr. Johnson’s large majority in the House of Commons should ensure that the tax increase is voted through on Wednesday. Furthermore, the tax increase is popular with voters who value the NHS. A YouGov poll found that 64% of voters backed higher levies to maintain the health service.

The government announced the NHS in England will get an extra £5.4 billion over the next six months to respond to Covid-19 and tackle the patient backlog. In the future, the government aims to use the extra cash to overhaul the social-care system, which is also straining after years of underinvestment and an aging population. The amount people have to pay for their own care will be capped at £86,000.

It is unclear whether the tax rise will be enough to put the NHS back on its feet. The Institute for Public Policy Research, a think tank, estimates the NHS needs extra funding of £15 billion a year, more than what the tax rise would generate.

Write to Max Colchester at max.colchester@wsj.com