Half a million illegal immigrants should be given the right to stay in Britain, a think tank has said.
Illegal immigrants could bring in £1bn in tax revenue
The Institute of Public Policy Research says such an amnesty would bring in £1bn in extra taxes, and save costs of £4.7bn needed to deport people.
It is urging Home Secretary Jacqui Smith to adopt the move, saying a large scale deportation would never happen.
The Home Office said an amnesty was unnecessary and would create "a strong pull for waves of illegal migration".
It is not known how many illegal immigrants are in the UK, with estimates varying widely from 300,000 to 900,000.
The Home Office has estimated it would take more than 30 years to deport them all.
Danny Sriskandandarajah, head of migration and equalities at the Institute of Public Policy Research, said: "The simple truth is that we are not going to deport hundreds of thousands of people from the UK.
"Our economy would shrink and we would notice it straightaway in uncleaned offices, dirty streets and unstaffed pubs and clubs.
"So we have a choice: make people live in the shadows, exploited and fearful for the future; or bring them into the mainstream, to pay taxes and live an honest life."
Immigration minister Liam Byrne has repeatedly rejected calls for an amnesty.
A Home Office spokesman said a new Australian-style points system for managed migration would allow skilled migrants into the UK to fill gaps in the economy.
Shadow home secretary David Davis said other countries who had granted such an amnesty "found it creates an unstoppable stream of illegal immigration".
"The state of our porous borders means that granting an amnesty for around 500,000 would quickly lead to thousands more taking their place," he said.
"The only long-term solution is to have an efficient asylum system so that we don't develop the huge back log from which this government now suffers."
The pressure group Migrationwatch UK has argued that an amnesty on illegal immigrants would put too much pressure on council housing.
The group has also questioned the benefits brought by legal migrant workers.
Chairman Sir Andrew Green said the latest government figures suggested the economic benefit from migrant workers worked out at about 73p a week for each person already living in the UK.
Trade unions recently said migrant workers who come to the UK legally had boosted the economy.
The TUC said the amount of tax paid by migrants exceeded the cost of supplying public services.