Theresa May has spoken with Jean-Claude Juncker and Angela Merkel following the decision
The British government has said it is "confident" of winning its appeal against the court ruling on triggering Brexit.
Theresa May has spoken with European Commission President Jean-Claude Juncker and German Chancellor Angela Merkel in the aftermath of the British High Court's decision.
Mrs May told them her plan to trigger Article 50, the formal process for severing ties with Brussels, remains on track.
Mrs May has pledged to begin Brexit by the end of March, but Thursday's ruling that she has to put it to the British Parliament first has raised questions about whether this will happen, and sparked calls for an emergency general election.
More pressure was heaped on the prime minister when Conservative MP Stephen Phillips announced he was resigning with immediate effect over "irreconcilable policy differences" with the government.
Mr Phillips, who has repeatedly called for Theresa May to reveal her Brexit plan to Parliament before starting the formal process of leaving the European Union, said he was "unable to properly represent" his constituents.
However, Downing Street is standing firm.
A spokesman said it did not accept the High Court judgement and was confident of victory in the British Supreme Court.
They said Mrs May explained to Mr Juncker and Mrs Merkel that "while the government is disappointed by the judgement yesterday, we remain of the firm belief that we have strong legal arguments ahead of the case which will be moving to the Supreme Court next month".
"The Prime Minister also confirmed that the planned timetable for notification of Article 50 remains the same."
Downing Street refused to say whether legislation was being drawn up for triggering Article 50 in case the appeal fails, stressing it was focused on winning the case.
When asked if Mrs May agreed with minister Sajid Javid, who said the judgement was "unacceptable", the spokesman replied: "The very fact that we are appealing that decision means very clearly that we don't accept that decision."
On Mr Phillips' resignation, a Number 10 source said he did not speak to Mrs May before quitting and added that the PM's position that there should not be an election before 2020 had not changed.
Speaking in Berlin after meeting the German foreign minister, the UK's Foreign Secretary Boris Johnson said he did not think the court decision would delay invoking Article 50.
When asked about the possibility of an emergency election, Mr Johnson told a news conference that people should not read too much into the legal decision.