A cross-party group of MPs is urging the Treasury to implement a new proposal that would help up to 3m people excluded from the UK government’s coronavirus support packages.

The gaps in support all-party parliamentary group, with more than 260 MPs, has developed a plan to help those ineligible for pandemic-related support — many of whom are suffering extreme hardship.

Millions have been unable to claim grants under the Self Employment Income Support Scheme (SEISS). They include company directors, people who did not file a 2018-19 tax return because they had just started working for themselves when the pandemic struck, or those who earned more than £50,000 or less than half their income from self-employment.

The group’s proposal would make previously excluded self-employed groups eligible for the next round of SEISS — which will be based on terms set out at the budget on March 3 — or a one-off grant of either £7,500 for the long-term self-employed or £3,500 for newer entrants. Company directors would receive either a one-off grant of £7,500 or be able to claim under another proposed system put forward by professional bodies, the “directors income support scheme”. This broadly mirrors the SEISS.

“[The government] promised to support people throughout the country and yet now, 10 months later, millions are still waiting for the first signs of support,” said Jamie Stone, a Liberal Democrat MP and chair of the APPG.

He urged the Treasury to consider the proposal, which he said MPs in the group favoured because it was “simple, fraud-proof, and quick to administer”.

The plan has been sent to the Treasury, which has indicated it intends to meet members of the APPG for further discussions. A Treasury spokesperson confirmed the proposal was under consideration.

Under the plan, those who had previously been able to claim Covid-19 support grants or who had been fined for breaking Covid restrictions would be excluded from receiving funds. Only company directors who are a “person of significant control”, have been trading the past three years, have been adversely affected by the pandemic and have projected trading profits for 2020-21 of less than £50,000 would be eligible.

Tax specialist Rebecca Seeley Harris, a former senior adviser to the Office of Tax Simplification (OTS) who developed the proposed plan, insisted it was workable. “They’ve got no real reason to not do something about this,” she said.

Treasury ministers have said repeatedly that in principle they would like to extend support to those who have missed out during the coronavirus crisis. But they point out that it is very difficult to draw up a workable scheme that captures the right people without running high risks of fraudulent claims.

The Treasury select committee on Wednesday held a hearing with tax experts on the gaps in Covid support measures. Caroline Miskin, from the Institute of Chartered Accountants in England and Wales, told MPs that the proposed directors’ income support scheme was “higher risk” than the existing SEISS, because it would rely to a greater extent on self-declarations from those applying.

She added that schemes already running in Scotland and Wales to help those who had missed out on support would be difficult to scale up because of the resources required to check evidence provided by claimants.

However, she and others giving evidence to the committee agreed there was no practical reason why the Treasury could not include more of the newly self-employed in the next round of SEISS grants, taking account of tax returns now being filed for 2019-20.

They also pointed out that ministers could change the terms of the SEISS to include those making less than 50 per cent of their income from self-employment, or taper payments to those with trading profits above £50,000, rather than excluding them entirely.

Esther McVey, the Conservative MP and former minister who co-chairs the APPG, urged the Treasury to take action. “We are talking about offering vital support to 3m people who, in one way or another, have made the leap towards running their own businesses.

“Abandoning this group sends out the message that Britain is abandoning entrepreneurs, those who see a gap in the market to create wealth and jobs for the country.”