Illegal immigration is likely to rise when Britain leaves the EU and freedom of movement ends, a new study has found.

The report by the Social Market Foundation said closing legal migration routes after Brexit would lead to more people trying to enter and stay in the UK illegally.

It said politicians who claim that Brexit will solve public concerns about immigration should "come clean" about the actual consequences of ending free movement.

Failure to do so would result in a backlash when voters realised that leaving the EU had not solved their fears about immigration, and risked “creating the sort of conditions in Britain that helped Donald Trump become US president”, the SMF said.

The study analysed previous cases where immigration was restricted and entry policies tightened, including Britain ending unrestricted migration from Commonwealth countries in the 1960s and the US stopping a programme for Mexican workers in 1965.

It found that stricter controls on immigration often led to an increase in the total number of migrants in the country, because people who could previously travel back and forth easily instead opt to stay.

Greater restrictions also fuel an increase in illegal migration as people who would previously have entered the country legally instead do so through other routes.

The SMF predicted that the number of people living in the UK illegally would increase after Brexit, as EU nationals who have not been given the right to remain in the country decide to stay without permission.

It called on the government to "inject a dose of honest realism, coming clean about the complexities and unintended consequences of immigration policy, about the control that it does have, but also the practical limits to that control".

The report warned that failure to do so would fuel fears about immigration. It highlighted the case of Donald Trump, who used growing concerns in the US about migration from Mexico to help him win the presidency, even though the number of Mexicans crossing the border has fallen significantly in recent years.

An immigrant's tale: Leaving Britain to escape Brexit hostility Show all 20 1 /20 An immigrant's tale: Leaving Britain to escape Brexit hostility An immigrant's tale: Leaving Britain to escape Brexit hostility Maria, 31, holds her daughters, Elena, two, and baby Ioana, weeks old, in her London home A few months after Britain voted to leave the European Union, Maria was told her to go back to her native Romania whilst in hospital by an elderly English woman. “You are a foreigner, your place is not here” recalls Maria, who was stunned Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Maria and her husband Adi, 37, take their daughters for a walk in Hampstead Heath near their home The couple are preparing to leave Britain later this year with their two children, fed up with what Maria says is xenophobia and the rising cost of living in London Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Elena holds up British passports belonging to her and her sister. Both children have dual citizenship, but their parents do not want to apply for this despite having permanent residency in Britain Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Maria holds daughter Ioana, who is less than a week old, while Elena wipes a table Maria had never faced direct abuse over her nationality in her 10 years in the country until that moment at the hospital Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Adi spends time with his daughters Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Adi plays hide and seek with his daughter Elena Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Food is served Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Adi takes his daughter, Elena, to nursery Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Adi's sister, Nicoleta, 34, carries her niece Elena in a restaurant after a trip out Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Adi and Maria cook together at their home Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Adi holds his baby daughter, Ioana Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Adi and wife Maria take their daughters for a walk in Hampstead Heath Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Berwyn, a neighbour of the couple, who moved to the UK in the 1980s from Australia, says goodbye to Maria after a visit at her home. Berwyn has dual citizenship - Australian and Irish as she lived in Ireland for a few years before moving to Britain. She calls the family her 'dearest Christian Romanian friends' Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Religious pictures including a portrait of Arsenie Boca, a Romanian Orthodox monk, theologian and artist (top), hang on the wall at the home of Adi and Maria Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Maria dries Elena after giving her a bath after nursery Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Maria holds her baby daughter Ioana Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Adi works with his colleague Alexandru, who is also from Romania, for a removal company Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Maria holds her daughter Elena Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Neighbour, Berwyn, holds baby Ioana Reuters An immigrant's tale: Leaving Britain to escape Brexit hostility Adi and Maria, along with their daughters, leave St Andrews church in Kingsbury after attending a service Reuters

Jonathan Thomas, migration researcher at the SMF and author of the report, said: “History suggests that people who expect ending free movement to take away their worries about immigration are going to be disappointed. Illegal immigration has not been a big part of British debate in recent years but the precedents suggest it could soon be high on the political agenda.

“People who want to end free movement should be honest with the electorate about the possibility that it will create significant new challenges relating to illegal immigration. And people who support a liberal approach to immigration should engage constructively with the perfectly legitimate view that illegal immigration is a problem that policymakers should address.”

The think-tank’s director, James Kirkup, added: “If our leaders fail to have that honest conversation about the future of immigration after free movement ends, they risk creating the sort of conditions in Britain that helped Donald Trump become US president.

“There are too many people in British politics, in all parties, who believe an open approach to immigration is beneficial but fail to talk honestly to voters about the pros and cons of immigration. They should ask themselves what Nigel Farage and the Brexit Party could become in future if misplaced expectations trigger another political backlash over immigration."

The government has already announced plans for a major immigration shake-up when Britain leaves the EU. Under the new system, which will prioritise workers with skills the UK needs, a new route for temporary workers will be created and an annual cap on skilled work visas will be scrapped.

A Home Office spokeswoman said: "The future immigration system will ensure the UK can continue to attract the talented people we need whilst bringing free movement to an end.

"For the first time in a generation, we will have full control of our immigration system.