The figure comes from internal Treasury modelling presented to Prime Minister Andy Burnham and Chancellor John Healey on Wednesday, according to Government sources.
Officials stressed that the 0.3 per cent forecast is based on a more extreme scenario and that the Treasury routinely models a range of possible outcomes.
The warning comes as Britain is already struggling with modest economic growth, while the conflict in the Middle East has pushed up energy prices and knocked consumer confidence since February.
Separate modelling shown to the Prime Minister and Chancellor suggested the economy could grow by 0.9 per cent this year if no permanent peace agreement is reached between US-Israeli forces and Iran.
As borrowing has climbed, investors have demanded higher returns for purchasing government bondsPA
The Office for National Statistics (ONS) is also expected to publish its latest economic figures on Thursday, with GDP forecast to have recorded no growth in June.
A consensus of economists expects the ONS to confirm on Thursday that the economy grew by 0.4 per cent in the second quarter, despite the flat June. That would follow a 0.6 per cent expansion in the first three months of the year.
Rob Wood, chief UK economist for Pantheon Macroeconomics, said this would demonstrate “the big picture is that the economy has remained resilient to the hit from the war in Iran”.
The services sector, which dominates the British economy, showed improvement in May, with professional services and scientific research and development leading the way.
Manufacturers and factory operators have also been building up stockpiles in preparation for potential supply shortages and price increases, a trend that has helped prop up growth figures in recent months.
However, a weaker picture appears to be forming from June onwards, with heatwaves producing mixed results for businesses and mounting pressure on some industries.
Mr Wood expects monthly GDP to have dipped by 0.1 per cent in June, “reversing the 0.1 per cent gain in May, as a sharp fall in construction activity drags on growth, while services and industrial production stagnate”.
Thomas Pugh, chief economist for RSM UK, said he believed the services industry was likely dragged down by falling hospitality activity, even with the Fifa World Cup getting under way in June.
His firm’s own business surveys suggest “consumers were likely switching away from restaurants towards pubs to watch the World Cup, rather than increasing the total amount of spending”.
Mr Pugh takes a slightly more optimistic view of June, forecasting monthly GDP to have edged up by 0.1 per cent.
He said: “All told, we expect GDP to nudge up in June, helped by a big jump in erratic mining activity.
That will be enough to deliver 0.4 per cent growth for Q2, as strong momentum from Q1 and consumers smoothing through higher inflation helped to support solid growth.”
He added that July could bring a further lift to activity, pointing to the hot weather and England’s run to the World Cup semi-finals as potential drivers.
A positive quarterly reading would be welcome news for Burnham, who has pledged to deliver “growth in every postcode” across the country.
The Prime Minister opened a new government hub in Manchester in late July, dubbed No 10 North, where he plans to work one day a week as part of efforts to shift power beyond Westminster.
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