The government has missed a Conservative party target to set a “national living wage” of £9 an hour by 2020 following weaker than expected average pay growth across the British economy.

In an end-of-year flourish designed to woo low-paid workers after his election victory, Boris Johnson announced on Tuesday that almost 3 million people would benefit from an above-inflation increase in the national living wage to £8.72 from April.

However, the settlement falls short of a promise made by the then chancellor, George Osborne, in 2015 to raise the legal pay floor for over-25s to £9 an hour by 2020. Failure to reach that target will translate into lost wages of about £1,600 for a full-time worker next year, according to the government’s own estimates.

David Cameron’s government had expected a rapid acceleration in pay growth across the British economy when Osborne set a target for the wage floor to hit 60% of median earnings by 2020 – which was forecast to be £9.35 by the Office for Budget Responsibility, the government’s independent forecaster. Referring to the OBR forecasts in his July 2015 budget, Osborne said the minimum wage would be set to reach £9 an hour by 2020.

In setting the 2020 pay floor at £8.72 an hour, Johnson has hit the median benchmark, although this is only because the median wage – the average pay level for all workers in Britain – has not increased to the levels anticipated in 2015.

The Low Pay Commission, an independent body that advises the government on the national living wage, said in November that over the past five years, the target had fallen from £9.35 an hour to £8.67 an hour because of a “low level of wage growth relative to forecasts in 2015”.

Osborne promised in 2015 at the first majority Tory government budget for almost two decades that a full-time worker on the national living wage would experience a gain of about £5,200 in cash terms by 2020. However, the Treasury admitted on Tuesday that the gain was now only £3,680.

Nye Cominetti, an economic analyst at the Resolution Foundation, said recent increases in the minimum wage, while maintaining record-high levels of employment across the country, should be welcomed.

However, he added: “The fact that it’s over 50p an hour less than originally forecast back in July 2015 shows just how disappointing typical pay growth has been over the past five years.”

Average annual pay growth in Britain has accelerated in recent years, reaching 3.9% during the three months to May. However, it remains below the forecasts made by the OBR in 2015, while pay growth has also begun to slow recently to 3.2% in the three months to October amid heightened uncertainty over Brexit.

The 2010s have marked the weakest decade for wage growth since the end of the Napoleonic wars 200 years ago, while average pay after accounting for inflation is worth less than it was before the financial crisis struck in 2008.

The Conservatives’ failure to hit the 2020 target for the living wage raises questions over whether the party will be able to set the legal pay floor at £10.50 by 2024, as promised ahead of the election.

Sajid Javid, the chancellor, has set a target to raise the low-pay floor from 60% of median earnings in Britain to two-thirds, saying this would mean a national living wage of about £10.50 by 2024. However, the aim depends on average pay growth rising as anticipated.

The Tories faced criticism earlier this month after including a caveat in the Queen’s speech that the promise would only happen “provided economic conditions allow”.

Cominetti said: “While describing minimum wage targets in cash terms works well in election campaigns, it’s important that government takes a more pragmatic approach to minimum wage setting that accounts for a changing economy.”

Labour promised a real living wage of at least £10 an hour for all workers aged 16 and over immediately, in a policy to show it would move faster to support households than the Tories.

Margaret Greenwood, the shadow work and pensions secretary, said: “This announcement falls short of what is needed to help workers. It comes against a backdrop of an economy created by successive Conservative governments, which has left millions of people trapped in low-paid, insecure work over the last decade. Underpayment of the minimum wage is on the rise.”