The bosses of Sainsbury's, Marks & Spencer and Morrisons have said Britain's food and supermarket sector will need continued access to EU migrant labour after the country leaves the European Union.
Asked when the expat issue can be expected to be settled, Mrs May's official spokeswoman said: "This is an issue that we are very clear matters to Europeans here in the United Kingdom and Brits in Europe".
Maintaining access to the single market should also be a "vital priority" in the government's Brexit negotiations, it said.
In a move that will prove unpopular with many who voted to leave the EU, Mr Davis told MPs today that the Government would "of course" consider paying to secure access to the Single Market.
Mr Davis told MPs the "major criterion" was getting the best access for goods and services to the European market.
"That's not the same as thinking free movement of people as it now stands is a good idea". Aside from European Union citizens, the date 289,000 of the arrivals came from outside Europe while 77,000 Britons returned to live in the United Kingdom over the year.
Police statistics show hate crimes against immigrants have particularly surged in areas of the United Kingdom that voted for Brexit.
France and Ireland on Thursday vented their frustration at the British government's slowness in outlining its Brexit plan, saying that they wanted some clarity in the next few weeks.
Liberal Democrat leader Tim Farron said: "The Government are in an absolute mess".
"Ministers' comments seem to have been over-interpreted".
Davis said the government would consider its options during divorce negotiations with the trading block.
Mr Davis said the triggering of Article 50 was still "four to five months" away and that when negotiations begin the Government's position will be "very clear".
Davis said while Britain will be "ending free movement as it has operated before ... we won't do it in a way that is contrary to the national end economic interest". I've said that it won't be plain sailing and that there will be some uncertainty in the months ahead. It was captured by a news photographer in Downing St., home of the department's offices and the prime minister's residence.
In total, all signatories represent the four United Kingdom farming unions and 71 leading food businesses with a collective turnover of over GBP92bn (US$116bn) and employing over 925,000 people across the UK.
The latest official figures on immigration to the United Kingdom will be published today. "I think you will find the record reflects that".
Relations between the United Kingdom and the rest of the European Union have become increasingly heated on the topic.
Dutch Finance Minister Jeroen Dijsselbloem, who is also president of the group of euro-area finance ministers, warned that retaining single-market access would cost the United Kingdom more after Brexit.
Plaid Cymru's Lord Wigley urged the government not to take the United Kingdom out of the single market which, he said, would be "the kiss of death" for farmers in Wales.