LONDON (Reuters) - Britain may have to allow European Union migrants to come to the country without restrictions for several years after Brexit because of the scale of the challenge of setting up a new immigration system, a think tank said on Thursday.

The Institute for Government, an independent research body, said it was unfeasible for the government to implement a new system by April 2019, when Britain is due to have left the EU.

“The prime minister has recognized that an ‘implementation phase’ will be required post-Brexit,” the institute said in a report. “For immigration, this will require the continuation of free movement, possibly for several years post-Brexit.”

Concerns about immigration played a key role in the debate ahead of last year’s EU membership referendum, and were the driving force behind many voters opting to support Brexit.

Prime Minister Theresa May has promised she will reduce the numbers of migrants after Brexit, making the issue one of her priorities at the expense of Britain’s continued membership of the EU single market.

The Institute for Government said that while Britain would be free to introduce new border controls for EU citizens once it left the bloc, in practice any interim measures introduced while a permanent system was being drawn up would hurt the economy.

“Multiple changes increase the disruption to labor markets and administrative burdens,” the report said. “That means free movement will have to continue post-Brexit until the new regime is ready to go live.”

Furthermore, the report said the government would need up to 5,000 additional staff to process applications from the roughly 3 million EU nationals who currently live in Britain.