By Max Colchester and Jason Douglas

LONDON -- British Prime Minister Boris Johnson said he was planning a "New Deal" for the British people as part of a speech aimed at re-invigorating the U.K. and his premiership in the face of falling poll ratings, an economy in the doldrums and one of the worst death rates from Covid-19 in the developed world.

Mr. Johnson said Tuesday he would bring forward a GBP5 billion ($6.15 billion) investment plan aimed at kick-starting the economy, confirming his departure from the small-government legacy of his Conservative Party predecessor Margaret Thatcher.

He dubbed the plan a "New Deal," a deliberate echo of former U.S. President Franklin D Roosevelt's stimulus program from the 1930s. Though, contrary to advance extracts of his speech, Mr. Johnson didn't mention the Democratic president by name.

"It sounds like a New Deal," said Mr. Johnson, "That is how it is meant to sound and to be, because that is what the times demand."

Mr. Johnson cemented his hold on power in a December election in which he won seats in former industrial towns in the north and midlands of England that have traditionally backed the main opposition Labour Party.

In his speech Tuesday in Dudley, a former Labour stronghold in central England that recently flipped to his Conservative Party, Mr. Johnson returned to his election theme of "leveling up" these poorer areas of the country.

"I am conscious as I say all this that it sounds like a prodigious amount of government intervention," he said, standing behind a lectern carrying the slogan "Build, Build, Build." In a nod to traditional Conservative voters, he added "I am not a communist. I also believe it is the job of government to create the conditions for free-market enterprise."

The last few months have been tumultuous for Mr. Johnson. His government has struggled to tackle the Covid-19 crisis, which has killed over 43,000 people here. The prime minister, who himself was hospitalized with the virus, faces questions on why he initially delayed locking down the country and didn't fire a key adviser who flouted lockdown rules. There is also confusion over the suite of policies being rolled out to reopen an economy where economic activity has shrunk by at least a quarter since the virus first hit.

Mr. Johnson said it was too early to judge his government's response to Covid-19. "We got some things emphatically right," he said.

But since mid-March Mr. Johnson's approval ratings have dropped by 20 points to 43%, according to pollster YouGov. While his Conservative Party still leads in the polls, the newly appointed leader of the opposition Labour Party Keir Starmer is now more popular than Mr. Johnson.

The British leader is being hit by "a lack of coherence in policy and a lack of respect for the rules around lockdown," says Robert Hayward, a pollster and Conservative member of the House of Lords.

To try to steady the ship, Mr. Johnson is undertaking an overhaul of government.

The prime minister's announcement of GBP5 billion of accelerated spending on projects such as hospitals, road building and tree planting is modest -- about 0.2% of gross domestic product and compared with the government's current GBP928 billion spending plan for this year. But the government isn't planning to introduce a program of austerity to claw back the extra money spent to tackle the coronavirus crisis, Mr. Johnson said.

He also announced reforms to planning rules aimed at making it easier to build homes.

The government is shaking up the British civil service. The U.K.'s top civil servant will leave his post in September and Britain's foreign office is absorbing another department that dispenses international aid. The government aims to close the chapter on Brexit by having a trade deal in place with the European Union by the end of the year.

In the short term, Mr. Johnson's future looks safe. He has an 80-seat majority in Parliament following a big win in December's election. He isn't due to face another election until 2024.

To sustain his popularity with traditional Labour voters won during the most recent election, Mr. Johnson will have to blunt the economic effects of Covid-19, which looks set to hit the poorest regions hardest.

So far blue-collar voters have tended to "put their values ahead of their wallets," says Matthew Goodwin, professor of politics at the University of Kent. "Once you throw in an economic crisis, their agenda in politics begins to change," he says.

To date, Britain's spending to combat the new coronavirus has been on par with some European neighbors but below that of the U.S.

Support measures, including grants to stricken businesses and wage subsidies for workers on furlough, are worth around 4.8% of GDP in 2019, according to calculations by the Brussels-based economics think tank Bruegel. That compares with 4.4% in France, 13.3% in Germany and 9.1% in the U.S. Tax deferrals and loan guarantees to businesses represent another 17% of U.K. GDP, Bruegel estimates.

The country is still feeling its way out of the first wave of the pandemic with further reopening of pubs and restaurants planned for July 4. A regional lockdown in Leicester in central England was announced on Monday night following a flare up of infections. Schools still haven't fully reopened nationally and businesses have complained that visitors to the U.K. currently face a two-week quarantine.

Mr. Johnson is a formidable campaigner and might well bounce back from these early setbacks, says pollster Mr. Hayward. But other prime ministers have blundered early in their tenures and never recovered, he says. "It creates a frame of mind and a certain view," he added.

Write to Max Colchester at max.colchester@wsj.com and Jason Douglas at jason.douglas@wsj.com