A bullish Boris Johnson has sought to reassure Tory MPs queasy about his plan to suspend parliament by announcing he wants to “step up the tempo” of Brexit talks in Brussels.

After his chief negotiator, David Frost, met EU officials in Brussels on Wednesday, the prime minister said on Thursday that both sides had agreed to meet twice a week.

“I have said right from my first day in office that we are ready to work in an energetic and determined way to get a deal done. While I have been encouraged with my discussions with EU leaders over recent weeks that there is a willingness to talk about alternatives to the anti-democratic backstop, it is now time for both sides to step up the tempo,” Johnson said.

Downing Street is gearing up to resist efforts by MPs, lawyers and campaigners to frustrate his suspension of parliament. Johnson’s team face a battle on several fronts, with the Scottish court of session due to rule on Friday on whether proroguing parliament is unconstitutional and MPs drawing up plans to legislate against a no deal.

Downing Street believes it can defeat the legal challenge, if necessary in the supreme court, and it will use every parliamentary tactic available to frustrate the rebel MPs. “We’ve been very clear before that we will deliver Brexit by any means necessary and that remains the case,” said one Downing Street source.

Aidan O’Neill QC, acting for a cross-party group of 75 MPs and peers, told the Scottish court of session in Edinburgh that Johnson had trampled on more than 400 years of constitutional law by asking the Queen to prorogue parliament solely for political gain.

“We have a constitution ruled by law,” O’Neill told Lord Doherty, urging him to issue an interdict – a Scottish court order equivalent to an injunction – forcing the UK government to quash the prorogation order signed by the Queen on Wednesday.

Whitehall sources said the government was “pretty confident of our case” and would pursue it to the supreme court “if for some reason the judgment went the other way”.

Johnson’s ruthless approach was underlined on Thursday evening when the chancellor’s media adviser was abruptly sacked.

It is understood the special adviser, who had previously worked for Sajid Javid’s predecessor as chancellor, Philip Hammond, was dismissed on the spot by the prime minister’s aide, Dominic Cummings, and escorted out of Downing Street.

The dismissal followed the last-minute cancellation of a speech planned for Wednesday by Javid and comes a few days ahead of a critical spending review.

However, cracks appeared on Thursday in the government’s careful public justification for the suspension of parliament when the defence secretary, Ben Wallace, was caught on mic at a meeting in Helsinki on Thursday. Wallace, a longtime ally of Johnson, said: “Parliament has been very good at saying what it doesn’t want. It has been awful at saying what it wants. That’s the reality. So eventually any leader has to, you know, try.”

He continued: “Our system is a winner-takes-all system. If you win a parliamentary majority, you control everything, you control the timetable. There’s no written separation, so … you pretty much are in command of the whole thing. And we’ve suddenly found ourselves with no majority and a coalition and that’s not easy for our system.”

Downing Street later said Wallace “misspoke”.

Ministers privately admit the battle to block anti-no-deal legislation in the Commons next week appears all but lost, but efforts to frustrate the rebels is focusing on the House of Lords.

Opposition peers expect Tory peers to attempt to filibuster the legislation, which will need to have passed through all its parliamentary stages and received royal assent before parliament is suspended or it will fall.

Johnson has already suffered one setback in the Lords as George Young quit the Tory frontbench in the upper house on Thursday in protest at the decision to suspend parliament.

In his resignation letter, Lord Young, who was a minister under Margaret Thatcher, said he was “very unhappy at the timing and length of the prorogation, and its motivation”. He said he was not part of any “remainer plot”.

It is unclear how Johnson would respond if an anti-no-deal bill is passed mandating him to extend article 50, but it is widely believed at Westminster that No 10 is working on plans for a general election to be held after 31 October if possible but beforehand if necessary.

Cabinet ministers who have previously been outspoken in their opposition to prorogation, including Amber Rudd and Matt Hancock, have been kept onboard by the hope Johnson can strike a reworked Brexit deal. They believe the real prospect of a no-deal Brexit will strengthen his hand in the negotiations and then persuade sceptical Labour MPs to support a deal rather than risk crashing out on 31 October.

According to a diplomatic note of Frost’s meeting in Brussels, seen by the Guardian, Frost downplayed Johnson’s suspension of parliament, describing it as normal. He told his interlocutors that Johnson wanted a deal but was not afraid of no deal.

The UK government appears to be seeking to convince the EU that it can bounce parliament into accepting any rewritten deal. Frost told EU officials that it would be possible to ratify a Brexit deal in the second half of October and argued that a technical extension would not be necessary. This strategy matches Johnson’s pledge to leave the EU on 31 October “do or die”.

EU diplomats remain sceptical that a solution to the thorny question of the Irish backstop can be devised in a mere 62 days. The EU’s chief Brexit negotiator, Michel Barnier, repeated his pledge that the bloc would stand by Ireland. “In all circumstances, the EU will continue to protect the interests of its citizens and companies, as well as the conditions for peace and stability on the island of Ireland,” he tweeted on Thursday. “It is our duty and our responsibility.”