Millions of people across Britain risk falling through gaps in the coronavirus wage subsidy plan and benefits system, according to two of the country’s leading economics thinktanks.

After ministers hurriedly pulled together plans to increase the level of financial aid available from the state as the Covid-19 outbreak intensifies, the Institute for Fiscal Studies said many self-employed workers would still get no support, while others would be left financially better off as a result of the crisis.

The Resolution Foundation thinktank also called on the chancellor to expand the universal credit benefits system to support more households.

Highlighting sizeable gaps in the government plan to pay 80% of employees’ salaries and self-employed workers’ profits as the crisis mounts, the IFS warns that 2 million people who work for themselves would not be protected because: they do not earn enough from self-employment to be eligible; earn more than the £50,000 threshold; or only started out working for themselves within the past year and therefore missing the threshold to prove their past income to receive wage subsidies.

A further 2 million more people who run their own company will also slip through gaps in the safety net deployed last week by the chancellor, Rishi Sunak, because they pay themselves much of their income in dividends, and less through a salary. A salary can be paid partially by the government, while dividends are excluded.

Offering an early glimpse of the divergent impact the coronavirus crisis will have for various groups in society, the IFS says a quarter of self-employed people will be financially better off than they otherwise would have been, even if their business is forced to shut down completely. This can happen if benefits income outweighs the 20% of lost earnings that are not covered by the state.

It says many of the self-employed whose incomes dry up will be able to receive universal credit now and 80% of their historical earnings for three months at the start of June. As these subsidies will also be based on past earnings, they could also be left financially better off.

However, workers who lose their job completely will not be helped by the schemes as more companies across Britain consider slashing jobs in response to the crisis, the IFS warns, while those who have to take unpaid leave to cover caring responsibilities, or who face a cut in their earnings but continue to work, could also be left worse off.

Although warning the measures are not as well targeted as would be expected in normal times, given the rapid onset of the crisis and the need to rush out support packages, the IFS says the average self-employed person and company employees would be better off than if the package had not been drawn up.

If employees are furloughed they will lose about only 12% of net family income, compared with 53% before the rescue measures. An average self-employed individual will lose about 14% of family income, compared with 44% before the changes were announced.

Stuart Adam, a senior research economist at 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.

“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.”

In a separate report, the Resolution Foundation has warned that some people will miss the receipt of benefits they could be eligible for. It also urges the government to help medium-income households by scrapping rules that lower the level of support for those with savings over £6,000 and rule out people with savings over £16,000.

Sunak said last month he would inject a further £7bn into the benefits system, raising the value of universal credit by £1,000 this year.

However, Karl Handscomb, a senior economist at the Resolution Foundation, said the government needed to bolster universal credit further to ensure the benefit system was “battle ready” for the economic fallout of coronavirus.

“The rollout of universal credit in recent years has been beset by controversy. But its performance over the next few months is the real test of this new benefit system, as it provides a living standards lifeline to millions of households.” he said.