May has said the divorce talks, likely to be the most complex in Europe since World War Two, would begin as planned next week and her Brexit minister, David Davis, said London's negotiating position was unchanged.
European Union leaders have been calling for talks to begin - on Tuesday Mr Barnier said: "I can't negotiate with myself".
Philip Hammond, Britain's finance minister, says protecting the British economy should be the main goal of upcoming negotiations over the country's exit from the European Union.
"Our view is that a withdrawal agreement and terms of the future relationship must be agreed alongside each other", a spokesman for Britain's Brexit ministry said.
The Queen's Speech was delayed and will now take place on Wednesday.
The Government have confirmed that Brexit Secretary David Davis will be in Brussels at the start of the week for meetings with the EU's chief negotiator Michel Barnier. "We know this would damage the capacity of the creative industries to deliver", Kampfner says.
"We would restore faith in politics if we could show that this parliament can at least function in presenting a view in the national interest which would command a majority on a cross-party basis", said veteran pro-European Conservative lawmaker Ken Clarke.
She declined to speculate about any change in Britain's plans to withdraw from the European Union following the election, saying, "The citizens have decided, and I assume that we will have to carry out these negotiations".
Mr Davis is expected to meet Mr Barnier at the Commission's headquarters in Belgian capital Brussels on Monday but it is not known how long the initial round of talks will last.
For another, the combination of finally launching talks on Monday and Ms May being at the summit on Thursday and Friday made the coming week a key opportunity to "rebuild trust" after tempers had boiled over on both sides in recent months.
Theresa May's failure to win a majority at the General Election has led to suggestions her Brexit plan to leave the EU's Single Market and Customs Union could be altered, while rival parties have demanded involvement in exit talks following the inconclusive result.
Critics of her approach have urged her to give ground in order to safeguard jobs and the economy.
With the United Kingdom still coming to grips with election result, Barnier urged London to appoint a negotiating team in order to start talks as soon as possible.