Brussels has warned that time is running out to start the talks on divorce terms and a future trade deal, with Britain set to leave the European Union come what may in March 2019.
"Next week, it will be three months after the sending of the Article 50 letter", Mr Barnier told the Financial Times and other European newspapers.
The Brexit negotiator askedLondon not to "waste time" and explained that it will take "several months to draw out the conditions of an orderly withdrawal, with hard and sensitive points of discussion".
Nigel Farage, former head of the eurosceptic UK Independence Party, admitted that after May's election disaster Britain is in a "very weak" negotiating position.
"And I confirmed to President Macron that the timetable for the Brexit negotiation remains on course and will begin next week".
Barnier also dismissed the idea of extended negotiations beyond the end date of March 2019, indicating he wants all discussions concluded by November 2018 at the latest.
Theresa May's disastrous election result has thrown the Brexit negotiations into question with no clear sense of when they will begin or what sort of Brexit and future relationship the United Kingdom is now seeking. Remaining in the single market was not what the electorate voted for, he said.
London has said it wants formal political talks between Barnier and Brexit minister David Davis to start next Monday but it since Thursday's election it has not formally committed to the date.
"The British government has said we will stay with the Brexit. That if Britain changes its mind it would find an open door", Guy Verhofstadt told the chamber.
Barnier's interview will heap yet more pressure on May, who called a snap general election to give her a stronger hand at the Brexit negotiating table.
May's Conservatives failed to win a parliamentary majority in an election last week, meaning it will need the support of Northern Ireland's Democratic Unionist Party to govern.
However, the potential deal has been met with considerable criticism in light of the eurosceptic DUP's controversial stance toward issues such as gay marriage and abortion, both of which they oppose.
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