European Commission President Jean-Claude Juncker (R) holds talks with British Prime Minister Boris Johnson in Luxembourg, Sept. 16, 2019. (European Commission/Handout via Xinhua)

LONDON, Sept. 16 (Xinhua) -- British Prime Minister Boris Johnson ended a hectic day in Luxembourg Monday insisting Britain will leave the European Union on Oct. 31.

Johnson held talks with President of the European Commission Jean-Claude Juncker. He gave an interview to British reporters to explain his side of how the day had progressed.

Johnson said there has been movement in talks in trying to find an alternative plan to the Irish backstop to avoid a hard border on the island of Ireland.

He said: "We are now at the stage where we need to start accelerating the work and that was the agreement today with Jean-Claude Juncker and Michel Barnier (the EU's chief Brexit negotiator).

"Yes there is a good chance of a deal, yes I can see the shape of it. Everybody can see roughly what could be done."

Johnson said: "I will uphold the constitution. I will obey the law but we will come out on October 31st. We're going to come out on October 31st and it's vital that people understand that the UK will not extend. We won't go on remaining in the EU beyond October. What on earth is the point?"

Ian Blackford, leader at Westminster of the Scottish National Party (SNP) was critical of Johnson's assessment, accusing him of being guilty of "dealing in fiction, not in facts".

He said the meeting between Johnson and Juncker confirmed the British government has failed to bring forward a single proposal to "end the Brexit mess". "Boris Johnson must stop dealing in fiction and start addressing the facts," he added.

On the events in Luxembourg, the EU said the aim of what was the first meeting between Juncker and Johnson was to take stock of the ongoing technical talks between the EU and Britain and to discuss the next steps.

The statement added that Juncker recalled it is Britain's responsibility to come forward with legally operational solutions that are compatible with the Brexit withdrawal agreement.

Juncker underlined the commission's continued willingness and openness to examine whether such proposals meet the objectives of the backstop.

"Such proposals have not yet been made," the statement said.

The statement added the European Council meeting on Oct. 17 will be an important milestone in the process, adding the 27 member states of the bloc remain united.

Juncker is to address the European parliament on Wednesday morning in Strasbourg, the statement concluded.

Luxembourg's Prime Minister Xavier Bettel went ahead with the media briefing, with the place prepared for Johnson left empty.

Bettel said the only solution that protected the EU's single market and prevented a hard Irish border was the Brexit withdrawal agreement that has already been rejected three times by politicians in Britain's House of Commons.

Johnson said he had cancelled attending the conference with Bettel because of concerns they would be "drowned" by protesters.

"I don't think it would have been fair to the Prime Minister of Luxembourg. I think there was clearly going to be a lot of noise," Johnson told British reporters.

In London, Downing Street described the meeting with Juncker as constructive, saying the pair agreed contact between Britain and the European Commission would be stepped up in the coming days.

Johnson's focus will switch Tuesday to the Supreme Court, Britain's highest legal chamber. A panel of judge will start to hear a case claiming that Johnson had been unlawful in the way he prorogued, or suspended, the British Parliament last week until Oct. 14.