The Chancellor has been accused of imposing “a stealth tax on middle England”.

The Daily Telegraph reported on Wednesday that half the income tax cuts in his Budget will be wiped out by a rise in National Insurance (NI) taxes.

So what’s happened here? And was there really a hidden NI hike in Philip Hammond’s Budget?

What did the Budget announce on income tax?

The Chancellor raised the higher rate threshold – the earnings level at which people will start paying the 40p rate of tax – to £50,000 from 2019-20.

This was a Tory manifesto pledge and Mr Hammond was able to introduce it a year earlier than previously expected.

Along with an increase in the personal allowance (the amount people can earn before paying any income tax) to £12,500, the Chancellor said this package would benefit 32 million people.

And what happened to National Insurance?

Nothing was announced by the Chancellor and there’s nothing about it on the Red Book “scorecard” produced by the Treasury listing all tax changes that raise or giveaway money relative to the previous baseline.

Yet some noted that the threshold at which NI payments are reduced from 12 per cent to 2 per cent had also risen to £50,000.

This means, according to The Telegraph, that higher-rate taxpayers will gain by £495, rather than the £860 boost they would have received if the NI threshold had been left alone.

Steven Cameron, pensions director at Aegon, was quoted as saying that: “The Chancellor was quick to showcase income tax savings in his budget speech but buried linked changes to National Insurance deep in the budget papers.”

And Sir Steve Webb, a former pensions minister, and currently director of policy at Royal London, said: “The Chancellor was keen to get plaudits for taking people out of higher rate income tax, but conveniently forgot to mention he was increasing National Insurance contributions. This can only be described as a stealth tax rise.”

So is this really a stealth tax?

This seems a bit of a stretch, given how the 2 per cent NI threshold has traditionally been linked to the higher rate income tax threshold.

Stuart Adam of the Institute for Fiscal Studies (IFS) described the increase in the NI reduction rate on Monday in line with its income tax counterpart as “completely normal practice”.

He said: “Of course, the government could always choose to decouple the two thresholds, but my normal expectation would be that they’d move in lock-step.”

The distributional analyses that the IFS produced on Tuesday, showing that the biggest cash gainers from the income tax changes were in the top 10 per cent of earners, took full account of the automatic NI threshold shift.

The IFS also has lower figures for the typical higher rate taxpayer gain than The Telegraph. It estimates that a typical higher rate taxpayer will benefit by £156 a year from the income tax threshold increase, while this would have been £291 without the NI offset.