As the economy slows, will all the Polish plumbers go home? This is an important question not only for those looking for someone to fettle their ballcock. It is also occupying the top brains in Threadneedle Street.

As Mervyn King, Governor of the Bank of England, pointed out yesterday, the booming British economy sucked in immigrants from Eastern Europe, restraining wage growth and keeping a cap on inflation. Now that the economy is slowing, could the process go into reverse?

Mr King painted a bleak picture, giving warning that inflation could top 4 per cent this year even as growth slows sharply. It was “quite possible” that the economy would be shrinking by the end of the year.

There were signs yesterday that the slowdown was feeding through into the labour market with the number of people claiming unemployement benefit rising 7,200 in April. Yet, average earnings including bonuses rose by 4 per cent in the three months to March, up from 3.7 per cent in the three months to February.

Many economists believe that the coming downturn will take the steam out of prices and prevent expectations of rising inflation from being baked into wage demands. They worry that the Bank may keep interest rates high for longer than is needed to curb inflation and may drive the economy down further than is necessary.

Given that its job is to look tough on inflation, the Bank unsurprisingly takes a less sanguine view on prices.

Which brings us back to the Polish plumbers, builders and shop assistants.

Since 2004, an estimated one million Poles have settled in Britain. But the slowing economy, the falling pound and a construction boom back in Poland have already persuaded some to return home. Many more are likely to follow.

Yesterday's gloomy comments from Barratt Developments, Britain's second-biggest housebuilder, reinforced fears of big cuts in construction jobs. Poles losing their jobs may simply head back to Warsaw.

That will reduce consumer spending, further depressing the economy, but without easing the pressure on wages.

If the Bank is right to be concerned about the impact of emigration, it would justify keeping interest rates higher for longer.

It would also make it a good idea to get that tap fixed sooner rather than later.

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