It is also calling for improved conditions for freelancers, the self-employed and zero-hour workers given the precarious nature of their work.
Rachel Flower, who is one of the national co-founders of ExcludedUK and lives in Huby, near Harrogate, said: "There is no question people have fallen into financial strife. Many will never forgive the Government.
“We have been working with the debt charity StepChange and other advice charities. Some are losing their homes and have been declared bankrupt.”
The Government has made an unprecedented intervention during the coronavirus pandemic to provide billions of pounds in support to prop up the economy amid the repeated lockdowns to contain the spread of Covid-19.
However, Gina Miller, the Co-Founder of the True and Fair Campaign, claimed that a two-tier economy is emerging after millions of workers who have not qualified for financial support.
She said: "It's a human and economic tragedy. These people are the hard-working backbone of the country and how do you come out of this crisis without them?
"The three million excluded are unable to support their families and pay into the public purse.
"The Government keeps making the excuse that it is too difficult. But everyone has a tax number...Many people have simply exhausted their funds."
Ms Flower said the Budget which was announced by Chancellor Rishi Sunak in March did include an extension of the scheme for the newly self employed.
She added: “This is a group of some 200,000 people who having set up in business in the 18 months prior to the pandemic were automatically excluded from the Self Employed Scheme back in March 2020, as they could not provide a 2018/19 tax return in accordance with the rules.
"We had called upon the Government during 2020 for this group of people to be able to claim a fair payment based upon whatever PAYE role they were doing in 2018/19, prior to becoming self employed - as they had paid taxes in full during that year and deserved fair support.
“These calls were ignored."
As a result of the recent extension to the scheme, this group can now provide their 2019-20 tax return as evidence of self employed status, Ms Flower said.
She added: "However, they can only claim future grants, they cannot back date them. This is a good example of how unfair this is - the Government now has evidence of their worker status, but is not allowing them to be on an equal footing with other self employed people who have claimed grants up to £2,500 a month since March 2020.
"For some, during the 2019-20 tax year, there will often be little profit because it will have been the company's first year in trading.
"The devil is in the detail, and that is what is so unjust about the way the schemes have been set up."
The Labour MP for Batley and Spen, Tracy Brabin, who is the co-chairwoman of the Gaps in Support All Party Parliamentary Group, said the package of support measures had been set up at speed, but there has been time for reflection to plug any gaps.
She said: "In West Yorkshire for example, there are an estimated 148,900 self-employed with 23,000 people employed in the arts and entertainment sector and the percentage of these people who are out of work is profound.”
She added: "For example, I heard from a DJ who said he has spent all his tax savings to live on, but now is required to pay the tax bill. There are many things which the Government could do if it had the political will.”
"It's heartbreaking to see talented people become lost to the creative sector, potentially never to come back."
Responding to concerns raised by Ms Brabin and other MPs, John Glen the Economic Secretary to the Treasury, told the Commons, the Government had spent £280 billion on schemes including the job retention scheme, which protected 9.6 million jobs.
He added: “Our overriding goal has been to provide as much support as we can to people and businesses, and as rapidly as possible. We acknowledge that we have not been able to help everyone in the way that we would ideally want to, but that has not been a wilful disregard for their situation.”
In reply to ExcludedUK, Jesse Norman, the Financial Secretary to the Treasury, said the CJRS (Coronavirus Job Retention Scheme) had helped to pay the wages of people in 11.2 million jobs across the country, with more than £53 billion paid out in grants across the UK, protecting jobs that might otherwise have been lost.
SEISS (Self-Employment Income Support Scheme) has paid out almost £20 billion in grants to 2.7m self-employed individuals whose businesses have been adversely affected by Covid-19, a letter from Mr Norman said.
He added: "The Government has provided an unprecedented package of measures throughout this pandemic to protect people’s jobs and livelihoods and to support businesses and public services across the UK, spending over £407 billion over this year and the next.
"The Chancellor announced at the last Budget the extension of the CJRS and SEISS until September.
"As part of this announcement, the Government has extended the Real Time Information (RTI) cut-off date for CJRS from 30 October 2020 to 2 March 2021, so that those employed on March 2, 2021, are eligible for claims starting on May 1, 2021."