The taoiseach, Leo Varadkar, was responding to criticism from Arlene Foster, leader of the Democratic Unionist party (DUP), who in turn had been reacting to his comments last week suggesting that the United Kingdom crashing out of the European Union could increase the chance of Ireland being reunited.
MPs are unable to table a motion of no confidence before next month because the House of Commons is in recess until September 3.
The Irish prime minister said that attacks on him and his deputy Simon Coveney in some parts of the British press were nothing new.
His ruling Conservative Party has had its majority in parliament cut to just one, after losing a by-election in Wales.
Mr Cumming's set out the government's Brexit strategy through a series of briefings to civil servants and ministers.
In an intervention likely to be interpreted as a warning shot to the new prime minister and chancellor, the Bank cut its economic growth forecast for this year and next and warned that even in the event of a smooth Brexit there is still a one-in-three chance of a recession in the coming year.
The stark document also warns that a no-deal Brexit could trigger "consumer panic", food shortages and an increased security threat in the United Kingdom within a fortnight.
Mrs Foster also hit out at the prime minister of the Republic of Ireland, Leo Varadkar, of "Project Fear mark 2" after the Irish Central Bank claimed that a clean, no-deal Brexit would cost their country 34,000 jobs and destabilise the economy.
But Brexit uncertainties and concerns of a no-deal have impacted economic growth.
Mr Cummings said the Prime Minister would have the power to hold the election until after the UK's departure date.
It also suggests he is willing to keep his vow and deliver Brexit by "any means necessary".
During his trip to Belfast, Boris Johnson said he the United Kingdom would leave the European Union on October 31st "come what may". He added that he had spoken to the new United Kingdom prime minister, Boris Johnson, and had invited him to Dublin to hold further discussions "without any precondition".
In a hard-hitting article for today's Mail on Sunday, Mr Barclay argues that the European elections in May reconstituted the EU - meaning Mr Barnier's mandate to insist on the harsh terms of the Withdrawal Agreement is no longer valid.
Theresa May's failure to pass her deal in the face of trenchant opposition from MPs to the backstop led to the fall of her Government.
Reacting to the leak, Fianna Fáil's agriculture spokesperson, Charlie McConalogue, said: "The document confirms what we already know regarding what the impact of a hard Brexit would be on the agricultural sector between the North and South".