“We have introduced and extended the National Living Wage, so that full-time workers are £4,000 better off each year.”

That was the claim from Dominic Raab, who was standing in for Boris Johnson at Prime Minister’s Questions this week.

The Conservatives introduced the National Living Wage in 2016. For most people on low pay, it replaces the National Minimum Wage.

We understand the £4,000 figure was reached by comparing the gross annual earnings of someone working 35 hours a week, 52 weeks a year, on the 2015 National Minimum Wage (£12,194) versus the same hours worked on today’s National Living Wage (£16,216).

But the figure does not account for inflation. We estimate that the real-terms increase is much lower: £2,777 over the same period.

And Mr Raab made another claim about workers’ take-home pay:

“Under this Government, we have cut income tax, saving every worker £1,200 each year.”

We understand he’s talking about the Conservatives’ record since they first took office in 2010. Back then, the “personal allowance” (the amount you can earn before you start paying income tax) was £6,095 a year.

Since then, successive Conservative chancellors have increased the personal allowance threshold. It now stands at £12,570.

As the independent think tank, the Institute for Fiscal Studies (IFS), explained to FactCheck, the increase in the personal allowance has saved the basic rate taxpayer (someone in the lowest income tax band) £1,219 a year.

But there’s a catch. This £1,219 figure doesn’t account for inflation. Once we do that, the saving is rather more modest: £1,009.

And there’s more.

The IFS points out that the government has legislated to freeze the personal allowance for four years, which is a real-terms increase in tax.

The think-tank told us: “back when the freeze was announced in March we said it was a 7% real terms cut in the personal allowance. That would equate to something in the neighbourhood of £175 per year in higher tax for a basic rate taxpayer. However that 7% figure was based on the [Office for Budget Responsibility’s] inflation forecast at the time – inflation has exceeded their forecast so far, so the real terms tax rise might end up being bigger too.”

The government was contacted for comment.

FactCheck verdict

Dominic Raab said workers are now better off by £4,000 a year thanks to the National Living Wage, which was introduced in 2016. But we estimate that with inflation in the mix, the wage rise is about £2,800 a year over the period.

Mr Raab also said that workers pay £1,200 less in income tax than they did when the Conservatives took office in 2010. But again, the saving is more modest once we adjust for inflation: £1,009. And he neglected to mention that the government has legislated to freeze the personal allowance for four years, which looks set to create a real-terms tax hike for workers of £175 a year, according to the Institute for Fiscal Studies.