Two million self-employed people could fall through the cracks of the government's coronavirus support package, a new study has warned.

Experts at the Institute for Fiscal Studies (IFS) warned that while some people could actually end up better off because of the crisis response many still risk getting no support.

They  said it was inevitable that measures put in place so quickly were not as well targeted as expected in normal times and

The Job Retention Scheme (JRS) and Self-employment Income Support Scheme (SEISS) were generous on average, replacing more than 80% of net family income for employees and the self-employed, but there was a lot of variation, said the research group.

The SEISS will not cover all of the 5.1 million people who report positive self-employment income, said the IFS, estimating that 1.3 million people with some self-employment income will be ineligible because they received less than half of their income from self-employment.

Chancellor Rishi Sunak drew up the schemes at a speed rarely seen in government

Around 225,000 will be ineligible because their self-employment profits were more than £50,000 a year, and 650,000 will be ineligible because they started their business since April 2019, said the IFS.

"These three groups overlap, so our rough estimate is that in total around two million people with some self-employment income will not have it covered by the SEISS," said the report.

Stuart Adam of the IFS said: "Under pressure to come up with a workable scheme to support the self-employed at speed, the Chancellor has erred on the side of generosity for most.

"Being able to claim the full amount even if profits are affected only marginally will leave some self-employed benefiting substantially.

John McDonnell has said the government must quickly move to fix the issue

"The delay in payments will cause financial hardship for some, but the fact that they can claim benefits for the next three months, and then also claim the earnings replacement in early June, will mean many will ultimately lose little or no income overall.

"But some will fall through the gaps completely, including high earners and the newly self-employed, and others will see only part of their overall earnings covered, including many who combine self-employment with employment or whose business is set up as a company."

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Shadow chancellor John McDonnell said the Government should now urgently revisit both schemes.

"It is unacceptable that carers, those on shorter working hours, and new starters who began work after February 28 are not covered by the job retention scheme, and that two million self-employed people are not covered by the self-employment package.

"We urge the Government to consider proposals that we have put forward to adjust the support schemes so that no workers are left behind in this time of deep anxiety for so many."