The Conservative Party’s four leadership candidates have been speaking at the party’s conference in the contest to succeed Rishi Sunak.

We have checked claims made by each of them.

Kemi Badenoch was asked about the previous Conservative government’s pledge to scrap thousands of EU laws by the end of 2023.

To minimise disruption following Brexit in 2020, the UK incorporated thousands of EU laws into UK law.

Ms Badenoch told Conservative members: “We did axe 4,000 [laws]”.

This is not right.

It was Badenoch – the trade secretary at the time – who announced in May 2023 that only 600 EU laws would be axed by the end of 2023, with another 500 financial services laws set to disappear later.

All other EU legislation was kept, unless ministers subsequently used other powers to change it.

Speaking about net migration, James Cleverly told the conference: “I got it down by 300,000 people a year”.

Mr Cleverly was home secretary between 13 November 2023 and 5 July 2024.

In December last year he announced rule changes on visas for overseas workers, students and their families, which he said would cut net migration by 300,000.

But we can’t yet say whether he achieved that – because the official net migration figures for 2024, which are published by the Office for National Statistics (ONS), are not available.

Net migration – the number of people coming into the country, minus the number of people leaving – reached a record high of 764,000 in 2022 and fell back slightly to 685,000 in the latest figures for 2023.

The ONS will publish the figures for the 12 months to the end of June 2024 next month.

Robert Jenrick talked about rising energy prices, which he said had caused factories to close and families to suffer.

“This is all because we have become so reliant on expensive forms of energy like offshore wind,” he said.

It is not true to say that offshore wind is the driver of high energy prices.

In the UK, electricity prices are usually determined by the price of gas.

For this reason, when gas prices spiked in 2022 following the Russian invasion of Ukraine, electricity prices rose sharply as well.

While offshore wind was relatively expensive in the 2000s and early 2010s, it has generally been getting cheaper since.

As a result, the National Infrastructure Commission said last year that the “cost of renewable electricity, through offshore wind, onshore wind and solar, is lower and less volatile than producing electricity with natural gas”.

The government’s independent adviser, the Climate Change Committee, has also said that the most effective long-term way to cut energy bills is to move away from fossil fuels.

And in a global report earlier this year the International Energy Agency concluded that the “rapid rollout of clean technologies makes energy cheaper, not more costly”.

Tom Tugendhat has repeatedly made this claim about his record as security minister.

He took on that role in September 2022 and held it until the election, almost two years later.

The National Security Act was passed in July 2023 and came into force last December.

No publicly available data shows what its effects have been so far, so we cannot tell whether Tugendhat’s claim is correct.

It includes provisions about threats to national security from espionage, sabotage and persons acting for foreign powers.

The Home Office wasn’t able to give us a number of arrested agents and suggested we ask the police instead.

The Metropolitan Police told us to submit a Freedom of Information request, which we have done.

The Home Office has previously told us that anyone charged with an offence under the National Security Act would still be part of an active legal process, so anyone involved would only be an alleged agent.

The Justice Ministry also didn’t have data on arrests and told us that any court data by offence wouldn’t include what Act the prosecution was brought under, or the defendants’ identity as a “Chinese or Russian spy”.

We’ve approached Tom Tugendhat to ask for more details but haven’t heard back.