The UK is not about to "suddenly shut the door" on low-skilled EU migrants, Brexit Secretary David Davis has said.
He warned it would take "years and years" for British workers to be in a position to take jobs now done by people from other member states.
"In the hospitality sector, hotels and restaurants, in the social care sector, working in agriculture, it will take time - it will be years and years before we get British citizens to do those jobs," he said.
"Don't expect just because we're changing who makes the decision on the policy, the door will suddenly shut: it won't," Bloomberg quoted Mr Davis as saying in the Estonian capital Tallinn.
Mr Davis said migrants had helped make the UK a strong economy.
"We're a successful economy, largely or partly at least because we have clever people, talented people come to Britain," he said.
"Even on the wider area, where we've got less well-paid people who have come to live and work in Britain, that will take time."
The remarks look likely to provoke questions from some hardline Leave supporters after Prime Minister Theresa May insisted that taking back control of immigration would be a key change after Brexit.
The Government says reducing net migration to below 100,000 a year remains its target.
Referring to the Brexit Secretary's comments, former Tory leader Iain Duncan Smith told The Times: "My sense is that it is going to happen quicker than that."
Mrs May has made it clear that transitional arrangements could need to be imposed on certain parts of the economy after Britain formally withdraws from the EU.