The Brexit fallout moves to Brussels on Tuesday as European leaders meet to discuss how best to proceed, and what the next steps should be as the UK walks away from the EU.

Taoiseach Enda Kenny will update a shortened Cabinet meeting this morning on the issue before he flies to Brussels. As Pat Leahy reports this morning, Kenny will urge his fellow leaders to show restraint towards Britain, with some in the EU in an unforgiving mood.

British prime minister David Cameron will attend a meeting of leaders on Tuesday night, but will be excluded from a meeting of the other 27 leaders on Wednesday, as they begin the process of proceeding without Britain. Mr Kenny's task is to maintain Irish interests, which will involve siding with Britain on occasion, given the close ties, economic and otherwise, between the two countries.

There is no clarity on what type of relationship Britain will seek with the EU when it is outside the union, although the Norwegian model of having access to the single market – even if this is unlikely to bring about the drastically reduced levels of immigration promised by leave campaigners – is emerging as a favoured option.

Some of those in Dublin have little confidence the institutions of the EU will recognise the body blow the union has been dealt, with one who has experience working in Brussels comparing the attitude of those in the European Commission and European Parliament, in particular, to the "last days of the Raj".

In his speech to the Dáil on Brexit, it was notable that Kenny again emphasised the primacy of the European Council – the forum of the heads of state and government that sets the EU's political direction – in the Brexit process.

In Berlin on Monday, Chancellor of Germany Angela Merkel, French president Francois Hollande and Italian prime minister Matteo Renzi set out their positions on how Europe should proceed.

On the issue of when the UK should invoke Article 50 of the Lisbon Treaty and begin formal exit negotiations, Ms Merkel is not as impatient as Mr Renzi and Mr Hollande.

As Derek Scally notes in his analysis, Merkel will not rush anything. Scally also points out that Berlin is not in the mood to punish Britain, all of which should help the case the Taoiseach is expected to make to his fellow leaders.

Waiting for Westminster

Of course, if the British wish that the formal Brexit negotiation process is delayed until a new prime minister is in place is agreed to by other EU leaders, there will be no progress at a European level until the political crisis in London is resolved.

Moves are quickening on that front with nominations for the Tory leadership closing on Wednesday. George Osborne, the Chancellor the Exchequer who was just months ago being talked of as David Cameron's natural successor, has on Tuesday morning announced he will not be a candidate.

Mr Osborne’s reputation was shredded among Brexiters in the Tory party by his warnings of economic shock in the event of a leave vote, warnings that now seem prescient.

The Times of London reports that Boris Johnson is not a sure thing to succeed Cameron. A YouGov poll for the newspaper finds Theresa May, the home secretary, is the more popular choice among Conservative voters.

Andrew Mitchell, a former Tory chief whip, told BBC's Newsnight that the early favourite never wins in Conservative leadership races. While Boris may yet become this generation's Michael Heseltine, Janan Ganesh argues that it is a democratic imperative that a Brexiter takes over the UK government. Ms May was a reluctant remainer.

The 1922 Committee of the Tory party set September 2nd as the date when the leadership contest will conclude and a new prime minister appointed. The party rules are that two candidates go forward from the parliamentary party for a run off with the wider membership so we can look forward to a summer of hustings.

The UK Labour party, meanwhile, is also in turmoil with leader Jeremy Corbyn facing a motion of no confidence on Tuesday, although it is non-binding.

Faced with mass resignations from his front bench, Mr Corbyn has dug in. He received a huge mandate from the Labour grassroots last summer and the parliamentary party’s only hope of unseating him is to agreed on a “stop Corbyn” candidate to go before the grassroots.

Faced with this mass revolt, Mr Corbyn last night called a snap rally of his hard left, largely Troskyist supporters outside the Houses of Parliament, causing further despair in the PLP.