Rishi Sunak will have to spend up to £4bn more on pensioners from next year if he sticks to the Conservative party’s “triple lock” pledge, despite refusing to boost funding for schools or welfare as he attempts to tighten the nation’s purse strings.

Anomalies in wages data pushed the headline growth rate of average UK earnings up to 5.6 per cent in April, with economists forecasting that the rate will rise to about 8 per cent by July.

If the chancellor sticks to the Tories’ triple-lock vow — which ensures that state pensions rise annually by the highest out of average earnings growth, inflation or 2.5 per cent — the government will have to increase pensions by the headline rate in July. The Office for National Statistics and economists say that the true rate of earnings growth is much lower.

The Treasury hinted that the government faced a difficult test on the issue, saying that its focus was to “ensure fairness for both pensioners and taxpayers”.

The department added that Thérèse Coffey, the secretary of state for work and pensions, would decide the new rate of state pensions in her annual review this year, but the final decision will be made by Sunak and Boris Johnson, prime minister.

Pensioners received the default 2.5 per cent increase this April. But pay rates have been distorted by growth being compared with last year when millions of people were receiving just 80 per cent of their salaries on the furlough scheme.

The level of average earnings has also been artificially raised because most jobs lost during the pandemic were in low-paid sectors. The National Institute of Economic and Social Research (NIESR) forecasts that growth in average earnings will hit 8.1 per cent in the second quarter.

Underlying wage growth is much weaker than the headline measure suggests. The ONS estimates that it averaged about 3 per cent in the three months to April, and NIESR forecast that it would average 2.5 per cent in the second quarter.

With the triple lock in place, the government’s £85bn-a-year basic pension costs would rise next April much faster than the income of the average working-age adult — especially given the government’s plan to end a temporary £20 uplift to the basic rate of working-age benefits in the autumn.

Each percentage point increase in the state pension represents a permanent increase of about £800m a year to spending on pensioner benefits, according to the Office for Budget Responsibility, the independent fiscal watchdog.

NIESR’s forecasts suggest that the government could spend up to £4bn a year more than necessary to keep pensioners’ living standards in line with those of working adults.

The Treasury’s choice on pensions will be compared with its refusal to countenance a one-off outlay on catch-up education spending, agreeing to just a tenth of the level recommended by the government’s adviser.

Sir Steve Webb, partner at the consultancy LCP and a former pensions minister, said that pensioners should not expect to have their income linked to average earnings growth this year. “If the point of the earnings link is to make sure pensioners don’t fall behind the rest of the population, the government has got to do something,” he said.

Sarah Coles, a personal finance analyst at Hargreaves Lansdown, said one option was for the government to tweak the way it calculated the increase in pensions, smoothing earnings growth over a longer period. This would avoid a huge increase “when the working population will probably be still clawing their way back from the economic effects of the crisis”.