Rishi Sunak and Keir Starmer faced each other in their first televised debate of the election campaign and traded claims on tax, the NHS and small boat crossings.

BBC Verify has been examining them.

Like the Conservatives, Labour has promised not to increase income tax, National Insurance or VAT during the next Parliament, but Rishi Sunak said: “Independent Treasury officials have costed Labour’s policies and they amount to a £2,000 tax rise for every working family.”

That quote risks misleading people, and the prime minister mentioned the £2,000 figure nine times during the debate.

As well as the £2,000 figure being questionable, it’s really totting up more than £500 a year extra over four years, which is not what you would normally think of if somebody said your taxes were going up by £2,000.

The figure is based on adding up how much the Conservatives claim Labour’s spending plans would cost – using some dubious assumptions – and dividing this by the number of UK households with at least one person working.

The Conservatives say the costings have been worked out by impartial civil servants, but a letter seen by the BBC from the top civil servant at the Treasury says the calculation of Labour’s plans costing £38.5bn overall (and therefore £2,000 per household over four years) “should not be presented as having been produced by the Civil Service”.

James Bowler wrote: “As you will expect, civil servants were not involved in the production or representation of the Conservative Party’s document ‘Labour Tax Rises’ or in the calculation of the total figure used.”

The point is that while civil servants were involved with working out the costings of some individual measures, they were working within assumptions made by Conservative-appointed special advisers.

For example, one costing looks at Labour’s plan to have more services provided by the state instead of by private companies and it assumes that private companies are always 7.5% more efficient.

But the civil servants doing the costings warned they had “low confidence” in the use of that figure.

Labour has also disputed that some of the items in the dossier are their actual policies. We won’t know exactly what Labour’s policies are – and how they will be funded – until we see its manifesto, which has not yet been published.

Keir Starmer said during the debate that the dossier was based on “pretend Labour policies”, including “a mental health policy that isn’t the Labour Party’s policy”.

You can read more about the tax claim here.

Keir Starmer responded with a big number of his own, saying of Rishi Sunak: “He told us it’s their policy to get rid of National Insurance (NI) altogether – that’s £46bn.”

He’s right that abolishing workers’ NI would cost about £46bn.

But the prime minister has not said he would do this during the next Parliament.

He told MPs in May “we have a long-term ambition to keep cutting National Insurance”, and promised to “make progress towards that goal in the next Parliament”, but not to abolish it completely.

The chancellor has said it is something he would do when the economy has grown by enough to make it affordable and conceded that it would not happen before 2030.

The £46bn is one of a series of figures that Labour have compiled into a £71bn dossier, many of which are not Tory pledges for the coming Parliament.

You can read more about it here.

Rishi Sunak said “taxes are now being cut”, but Keir Starmer said taxes “are at the highest level for 70 years”.

They are both correct but are talking about different things.

The government has cut NI twice, saving an employee on the average full-time salary of £35,000 about £900 this year.

But at the same time, the amount of tax taken as a proportion of the size of the economy is expected to reach a 70-year-high in the next five years.

That is largely because the points – known as thresholds – at which we start paying tax and higher rates of tax have been frozen.

This means more people are paying tax and higher rates of tax, than if these thresholds had risen along with inflation.

It is important to point out that the thresholds are to remain frozen under both the Conservatives and Labour until 2028.

You can read more about it here.

Keir Starmer challenged Rishi Sunak to explain how NHS waiting lists are coming down if they’re at 7.5 million now compared with “7.2 million when you said you would get them down”.

Starmer is correct about those figures.

Waiting lists in England have fallen from their peak last September, but are still higher than when Sunak pledged to cut them, in January 2023.

Last September, waiting lists rose to a peak of nearly 7.8 million.

But as you can see in the chart below, they’ve fallen from that peak. So, Sunak was right to say “waiting lists are coming down” in that sense.

Talking about people arriving in small boats across the English Channel, Rishi Sunak said: “We got the numbers down last year by a third.”

That is correct – the numbers in 2023 were a third lower than in 2022.

But the number of people who have crossed so far this year is at a record high – up more than a third on the same period last year.

Mr Sunak went on to say: “Over the last 12 months, the number of crossings are down a third.”

That is not quite correct.

As of 3 June, the number of people detected crossing in the last 12 months was 32,338.

This was down by a quarter – or 11,043 people – from the previous 12 months – not by a third.