Rishi Sunak and Liz Truss are ramping up their campaigns for the Conservative leadership this weekend, announcing new policies to tackle NHS backlogs and scrap EU laws if they become prime minister.

First up, the former chancellor, who will promise to make cutting NHS waiting lists his “number one public service priority” if he wins the contest.

A record 6.5 million were waiting for a routine NHS hospital treatment in June – the highest number since records began 15 years ago.

The number of people waiting for more than a year for hospital treatment is almost 200 times higher than before the pandemic, with 300,000 in the queue at the end of February this year – compared to 2020 when that figure was below 2,000.

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In a speech in Grantham – the birthplace of former Conservative prime minister, Margaret Thatcher – Mr Sunak will pledge to create a “vaccine style taskforce” to “cut bureaucracy and waste, and drive radical reforms”.

He will say he would “eliminate one year waits” by September 2024 – six months earlier than the current government target – and ensure everyone who has been waiting more than 18 weeks for a procedure is contacted by their trust within 100 days.

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And in his “war footing” NHS plan, he will also promise to deliver 200 community diagnostics hubs by March 2024, offering things like MRI and CT scans, expand testing at home, and help patients choose their own appointment times.

Mr Sunak is expected to say: “Already many people are using money they can’t really afford to go private. That is privatisation by the back door, and it’s wrong.

“People shouldn’t have to make a choice with a gun to their head. If we do not immediately set in train a radically different approach, the NHS will come under unsustainable pressure and break.”

But staff are already feeling the strain from the pandemic and there are vacancies across the board, with Labour warning the government needed a plan to “tackle the workforce crisis” in the service if it wants to cut waiting times.

Meanwhile, in her latest policy pitch, Ms Truss promised a “red tape bonfire” of EU laws, pledging to review all the rules retained in the UK post-Brexit by the end of 2023.

The foreign secretary says she will then scrap or replace those which she believes damage economic growth to “encourage business investment” and “make the most of our new-found freedoms outside of the EU” – echoing promises by Boris Johnson.

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Ms Truss insisted she was the “best candidate to deliver on the opportunities of Brexit”, adding: “EU regulations hinder our businesses and this has to change.

“In Downing Street, I will seize the chance to diverge from outdated EU law and frameworks and capitalise on the opportunities we have ahead of us”.

Mr Sunak has already pledged to appoint a Brexit minister to go through the retained laws if he wins the contest.

He said they would be instructed to come forward with initial recommendations for rules to be scrapped or changed within 100 days of the former chancellor taking office.

There are currently more than 2,000 pieces of legislation that the UK has retained since leaving the EU, and Brexit opportunities minister Jacob Rees-Mogg had pledged to axe all the remaining laws by 2026.

But TUC general secretary Frances O’Grady said the leadership candidates’ “cynical and reckless proposals threaten hard-won workers’ rights”.

She added: “Holiday pay, equal pay for women and men, safe limits on working hours and parental leave are just a few of the rights underpinned by retained EU law. These are all essential – not a nice to have.

“Let’s call this out for what it is – ideological posturing at the expense of ordinary working people.”

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Liberal Democrat foreign affairs spokesperson Layla Moran echoed the point, and said the Conservatives “would do better to focus on fixing their botched trade deal with Europe, which is drowning our businesses in red tape and raising prices in the shops”.

Mr Sunak and Ms Truss were named as the final two candidates in the race to become the next Tory leader and UK prime minister on Wednesday after their rival, Penny Mordaunt, was knocked out of the race.

A member of Ms Mordaunt’s campaign claimed on Friday that there had been “nasty briefings” against her from both the remaining candidates, and warned them the tactic would “backfire in the long term”.

The winner of the contest is down to the Conservative Party membership, who will have until 2 September to cast a vote for their preference after six weeks of hustings and campaigning across the country.

The result will be announced on 5 September, with the new PM expected to replace Mr Johnson in Downing Street a day later.

In the meantime, Mr Johnson will remain as a caretaker prime minister in Number 10.