Theresa May will be pressed to give further details about her plans for Brexit when she appears before a panel of senior MPs.
The Prime Minister will make her first appearance in front of the Liaison Committee amid frustration from some MPs at the lack of information about the Government's stance before she begins the formal Brexit process by the end of March.
Mrs May told the Commons on Monday she has promised to keep pushing for an early deal on the rights of EU nationals living in the UK after being rebuffed by fellow leaders at last week's European Council.
The Prime Minister said that leaders of the remaining 27 states had made clear they were not prepared to enter discussions on the subject until she formally triggers withdrawal talks under Article 50 of the EU treaties.
Mrs May insisted her end-of-March timetable would remain in place even if the Supreme Court rejected the Government's appeal over its right to begin the Brexit process without parliamentary approval.
The PM said she had used the summit to reaffirm her commitment to a "smooth and orderly" exit, and to give reassurance "early on in the negotiations" to EU citizens living in the UK and UK citizens living in EU countries that their right to remain will be protected after Brexit.
"I made clear once again that I hoped that this issue of EU citizens living here and UK citizens living in the EU member states can be dealt with at an early stage of the negotiations," she said.
"The other member states and the council have been clear that they are not prepared to enter into negotiations before Article 50 is triggered.
"But I will continue to remind them of our hope, for a very good reason - we want to give certainty and reassurance to people that this can be dealt with at a very early stage and then the people concerned can get on with their lives."
Mrs May insisted she would trigger Article 50 by the end of March even if the UK's highest court decides parliamentary approval is required.
She said: "I'm clear the Government will respect the verdict of our independent judiciary. But I'm equally clear that whichever way the judgment goes we will meet the timetable I have set out."
Liaison Committee chairman Andrew Tyrie has asked Mrs May to set out what plans are in place for the financial services industry and other key sectors of the UK economy.
During the 90-minute session giving evidence to the panel, made up of the chairmen of the various Commons select committees, Mrs May is also expected to be challenged about the funding available for the NHS and social care.