Labour will call for the government to commit a £500m “winter bailout fund” for the NHS over the coming months, citing party analysis suggesting 10,000 people a day will wait at least four hours for A&E treatment this winter.

Jonathan Ashworth, the shadow health secretary, will announce at the Labour party conference in Brighton that NHS patients suffered their worst winter on record in Theresa May’s first year as prime minister.

“Last winter Theresa May stuck her head in the sand and refused to give the NHS the money it needed to keep services running properly,” he said before his speech on Tuesday. “This decision pushed NHS staff beyond their limits and caused misery for patients in every part of the country. It can’t be allowed to happen again.”

Ashworth said he had consulted with senior NHS leaders to arrive at the right figure for funding to help ease the winter months. “Everybody would agree [last year] it was one of the worst winters in the NHS for some time, we saw very emotive pictures of people in corridors and ambulances backed up outside,” he told BBC Radio 4’s Today programme.

“When you look at the data, the NHS performed very badly, the waiting targets were not met. We think extra funding is needed for extra capacity. The head of NHS providers was calling last week for something in the region of £350m. We’ve been speaking to people behind the scenes and we think £500m is the right figure.”

Ashworth said it was clear the NHS needed more funding long-term, repeating labour’s manifesto pledge of an extra £7bn for the health service, which he said “substantially goes further than the Conservatives” but said it would not be right to immediately commit to the 4% annual rise as seen under the last Labour government.

“I strongly believe as the health secretary, we should be giving the NHS 4% a year and I want us to work towards getting back to that,” he said. “But I cannot say on day one of a Labour government that it will definitely be 4%, because we have to manage the public finances prudently.

“An extra £7bn is a substantial investment. My ambition long-term would be increasing NHS funding by 4%, which experts generally agree is around the right figure.”

Ashworth will also announce a Labour review of NHS treatment for gambling addiction, including considering whether the gambling industry should be forced to pay a compulsory levy to fund treatment services. It would replace the current voluntary system.

The review, a joint initiative by Ashworth and Labour’s deputy leader, Tom Watson, will examine the ability of the NHS to provide effective mental health treatment for gambling addicts.

Watson will also address the conference on Tuesday and will accuse gambling companies of being “driven by greed”. He will suggest they are deliberately targeting poor communities.

“Children and young people are being targeted by betting advertisers more than ever,” Watson will say. “We now know that when vulnerable people try to opt out of online gambling, companies don’t always block their accounts, as they should.

“Gambling companies are even harvesting data to deliberately target low-income gamblers and people who have given up gambling.”

Angela Rayner, the shadow education secretary, will use her keynote speech to lay out a draft charter for a national education service. The service is intended to be “lifelong, providing for people at every stage of their life”, and free at the point of use.

Rayner will attack the Conservatives’ failed manifesto pledge to open new grammar schools, as well as the technical problems that have hindered the government in delivering new funded nursery places.

“The Tories promised free childcare to the children of working parents,” she will say. “They promised over 600,000 places. But they created less than a quarter of them. The most disadvantaged aren’t even eligible and costs are rising more than twice as fast as wages. Today we are publishing a report setting out the alternative.”