The UK economy could lose more than half a million jobs by 2020 in the event of a vote to leave the EU and would be unlikely to recover from the impact fully even after 15 years, the head of the CBI is set to warn.

Carolyn Fairbairn, director-general of the business lobby, will present research by PwC, the professional services firm, suggesting the shock of a British exit could cut economic output between 3 and 5.4 per cent in 2020, depending on what sort of deal Britain managed to negotiate with its trading partners.

In the CBI’s more optimistic scenario, per capita GDP would be 0.8 per cent lower in 2030 than if the UK stayed within the union.

“The economy would slowly recover over time but never quite tracks back to where it would have been. Leaving the EU would mean a smaller economy in 2030,” Ms Fairbairn will tell an audience at the London Business School on Monday.

Her intervention has provoked the ire of Leave campaigners, who say the CBI is presenting skewed evidence and has a poor record on EU matters after backing UK membership of the euro.

Estimating the impact on the economy of a vote to exit is difficult because no one knows what the alternative relationship with the EU and other countries would be. In addition, Out campaigners are not united on which model — Norway, Switzerland or Canada, for instance — they would prefer.

PwC looked at two scenarios in the event of “Brexit”. In the first, the UK would conclude a free-trade agreement with the EU but would not retain free movement of services, capital or labour. It would relax rules for highly skilled migrants but stop admitting low-skilled EU nationals.

In the second, negotiations would drag on and the UK would default to trading under World Trade Organisation rules while clamping down on migration.

In either case, the report found, a vote to leave would create huge short-term uncertainty, leading businesses to delay hiring and investment decisions. This would lead to a spike in unemployment and could have a lasting effect on the UK’s capital stock.

In the longer term, unemployment should fall back to about 5 per cent but lower migration could cause skills shortages. Even with a free-trade deal, PwC estimates non-tariff barriers could cut 0.5 per cent from GDP by 2030. Under WTO rules, the impact would be much bigger.

This would be partially offset by ending the UK’s contribution to the EU budget but PwC believes benefits from cutting regulation would be “fairly minimal”.

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In the gloomier scenario, GDP could be 3.5 per cent lower and per capita GDP 2.7 per cent lower in 2030 than if the UK had remained in the EU.

The report warns against overstating this finding, noting that the hit to GDP by 2030 represents a loss of only one or two years of trend growth. “The UK would remain a relatively large, affluent and growing economy in both our exit scenarios, just not quite as large or affluent as in the counterfactual.”

PwC chose not to look at alternatives such as the Norwegian or Swiss models, under which the UK would still have full access to the single market, arguing that retaining free movement of labour would be inconsistent with the thrust of the Out campaign.

It is hard to see circumstances under which the UK could secure a better set of deals on trade and investment outside the EU

Matthew Elliot, chief executive of Vote Leave, accused the CBI of using “deeply pessimistic” assumptions, in particular by omitting the potential for a deal on free trade in services.

However, Ms Fairbairn will argue that “even in the best case, this would cause a serious shock to the UK economy”, adding: “It is hard to see circumstances under which the UK could secure a better set of deals on trade and investment outside the EU.”

It has become increasingly uncomfortable for business leaders to intervene in the EU debate after John Longworth lost his position as head of the British Chambers of Commerce for voicing his personal views rather than those of his members.

However, the CBI says some four-fifths of its members, including a large majority of smaller businesses, want to stay in the EU, with just 5 per cent supporting Brexit.