When hundreds of thousands of eastern European migrants came to the UK after the EU expanded in 2004, official statistics did not spot the arrivals for a long time. It is fitting therefore that the Office for National Statistics now stands accused of also failing to notice an exodus of 1.3m foreign-born people during the pandemic, including 700,000 from London.

It is difficult to fault the logic of Jonathan Portes and Michael O’Connor, who have pointed out the absurdities in the latest official data. The ONS currently estimates that employment in London rose by 66,000 or 0.4 per cent over the most recent year, even though its own tax data and its benefit claimant statistics show the number of workers to have cratered.

The discrepancy arises from deficiencies in the Labour Force Survey, which the statistical agency uses to estimate employment. It assumes the population has not changed, so if it finds fewer foreign-born people in London to interview, it gives a higher weight to the UK-born Londoners it did contact.

There are two possible explanations for what is going on. Either the foreign-born people the ONS normally questions have gone to ground during the pandemic, or they have left. It is too soon to form an accurate picture, but all employment figures derived from the Labour Force Survey at present should be discounted.

The last time the ONS failed to spot a large shift in migration, the Bank of England was quick to act. Mervyn King, governor at that time, highlighted the short-term advantages of an influx of eastern Europeans.

In a 2005 speech, he noted that inflows of migrant labour were a shock-absorbing force for the economy. When spending was strong, it would attract workers from abroad and put less pressure on prices and wages.

“It is possible, indeed likely, that inflows of migrant labour have eased labour market pressure,” Mr King said, adding that “the reversal of the flows of migrant labour might reduce the downward impact of a softer labour market on wage costs”.

The pandemic has resulted in a much softer labour market, especially in the UK’s big cities. If large numbers of foreign-born workers have left, the short-term effects are likely to be beneficial both for the individuals and for the UK. If some migrants have decided going home during the pandemic is better than staying in London, they are better off. The UK ends up with a smaller rise in unemployment, a less crowded environment and cheaper rents, particularly in London.

The longer-term effects depend on what happens to the economy. If city centre jobs in restaurants, pubs, hotels and sandwich shops never return, the UK’s pool of unemployed workers would be correspondingly lower and easier to manage.

But if vaccines work, the economy bounds back and life returns to normal, Britain could have a big problem. EU nationals with settled status in the UK could still return, but Brexit’s end to free movement would gum up the ability of employers to hire new staff from the EU or elsewhere. That would be a classic non-tariff barrier to trade, likely to result in rising inflation and higher interest rates.

A worker shortage might result in a burst of labour-saving innovation in hospitality. That would leave the well-heeled able to pay for human service while machines dispense coffees and pints for the masses.

To have an idea of what the future holds, we really need to know how many people there are in the UK and the effect of the pandemic on those numbers. The 2021 census should help, but there is next to nothing the ONS is able to say right now. Fifteen years after the UK learnt it had shockingly bad population statistics, precious little has improved.