Almost one million people will be forced to work unpaid for six months if a new government work scheme is extended across the country, a thinktank has said.

Under the Department for Work and Pensions community action programme (Cap), which has completed a pilot stage and whose rollout is expected to be announced this autumn, people on jobseeker's allowance for longer than three years must work for six months unpaid or have their benefits stripped from them.

Two weeks ago the employment minister, Chris Grayling, flagged his intention to introduce the scheme – recently renamed support for the very long-term unemployed – across the country to tackle the rising number of chronic unemployed, driven up by a stagnant economy.

Under its lowest estimate, the Centre for Economic and Social Inclusion (CESI) predicts that over a five year period starting in June 2013, 1.78 million people will be unable to find work through the government's current two-year-long employment scheme, the work programme, even if targets are met.

CESI estimates that of those failed by that programme, 1.35 million will be claiming jobseeker's allowance (JSA) as opposed to sickness and other types of out-of-work benefits. A further 378,000 people will stop claiming even though they will not have found work. In total the thinktank predicts that between 2013 and 2018, 972,000 will stay on JSA who will have been completely out of work for more than three years and will be eligible to be sent to work for free for 26 weeks.

But if the economy continues to shrink, and current employment schemes fail to reach targets, the number eligible to be sent on the programme could reach 1.06 million.

Grayling told the Guardian that the programme's development was still at a very early stage and so any predictions would be "guesswork".

Separately, a 41-year-old jobseeker who refused to attend Cap on the grounds that it was "slave labour" is waiting to hear from the high court whether he was won a judicial review.

During the case last month the court heard that Jamieson Wilson, from the Midlands, was expected to wash and clean furniture for an unnamed organisation for six months unpaid.

After refusing to take part in the "exploitative" scheme, Wilson, who trained and worked as a mechanical engineer and an HGV driver and has been unemployed since 2008, was stripped of his benefits and was now "relying on family and friends" to survive.

A decision in the case, which could affect the outcome of all mandatory work schemes, labelled by employment campaigners as "workfare", is expected before 10 August.

Dave Simmonds, CESI chief executive, said rolling out Cap could prove to be a very expensive mistake.

"These numbers speak volumes about the nature of long-term unemployment in a recession, where those with the greatest barriers are often pushed to the back of the jobs queue.

"Jobcentre Plus and the work programme will have already tried to find jobs for these people – with sanctions hanging over them all the way through. We have to be careful about a one size fits all solution for the very long-term unemployed by requiring them to work for their benefits."

Referring to recent DWP research which showed that a one-month mandatory work scheme had "zero effect" in helping people get a job, Simmonds added: "It could prove to be a very expensive failure if it doesn't get people into jobs – and past evidence on this is mixed."

Speaking about the CESI forecast, Grayling said: "We believe that full time community work should be a part of the support we provide to the very long term unemployed. But we are at an early stage of trialling different options, and so these estimates are pure guesswork."