The summit comes amid continuing political deadlock in the region and after Northern Ireland Secretary Chris Heaton-Harris announced plans to extend a deadline for calling a Stormont election and to cut the pay of Assembly members.
The absence of a power-sharing executive means that Northern Ireland will not be represented by any politicians at the talks, with Jayne Brady, the head of the civil service there, attending instead.
It is rare for a British prime minister to travel to British-Irish Council summits. Mr Sunak will be the first to do so since Gordon Brown became the first UK leader to do so in 2007.
Opening the summit, the prime minister is expected to stress his commitment to the Good Friday Agreement and his hope that devolution can function again soon.
“We all want to see power sharing restored as soon as possible,” he will say.
“I’m determined to deliver that.”
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He will also use the occasion to urge closer collaboration, as he meets with Ms Sturgeon and Mr Drakeford, as well as Mr Martin.
“We face huge challenges from global economic headwinds to war in Europe,” the prime minister will say.
“So let’s be pragmatic. Let’s work together in our shared interests. Let’s deliver for all our people across these great islands — and build a future defined not by division, but by unity and hope.”
While at the summit, Mr Sunak will also host his first council with the heads of the devolved administrations to discuss next week’s autumn statement, with Chancellor Jeremy Hunt expected to join the discussion virtually.
Michelle O’Neill, vice president of Sinn Fein, who cannot attend proceedings due to the crisis at Stormont, said the summit represented a “test” for Mr Sunak.
“We’re aware that both the British Prime Minister Rishi Sunak and the Taoiseach Micheal Martin will be there together,” she said.
“So that’s an opportunity for a very strong statement and what I want to hear from Rishi Sunak tomorrow is actually his plan for how he’s actually going to restore this executive and have local ministers in place, his plan for how he’s going to advance and propel talks with the EU around getting an agreement on making the protocol work.”
The British-Irish Council is comprised of representatives from the British and Irish governments, the devolved administrations in Scotland, Wales and Northern Ireland and the governments of the Isle of Man, Jersey and Guernsey.
It was formed in 1999 under the British-Irish agreement, part of the Good Friday Agreement which brought an end to the period of violence in Northern Ireland known as "The Troubles".
The council's stated aim is to “promote the harmonious and mutually beneficial development of the totality of relations among the peoples of these islands”.
All eyes will be on the outcome of Mr Sunak's discussion with Mr Martin for potential progress on the Northern Ireland Protocol.
Chris Heaton-Harris, the Northern Ireland secretary, said he hoped the meeting would be “a very positive reset in the relationship” between the UK and the Republic of Ireland.
Speaking to LBC radio, he also expressed hope that relations between Britain and the EU would improve.
“The problems are that lots of goods now are not available in Northern Ireland that are available in England, Scotland, and Wales,” Mr Heaton-Harris explained. “And that’s because the European Commission insisted on essentially types of potentially, in the future, customs checks, because they worry about goods flowing from the United Kingdom into the European single market. So we absolutely believe we can fix this by sharing of data.”
Asked whether we will still be talking about the protocol in six months, Mr Heaton-Harris said he hoped for a resolution because “there are also many other important things to be talking about.”
He insisted that cutting the pay of all Stormont MLAs, rather than singling out the DUP members boycotting devolution, is “fair and proportionate”.
Ms O’Neill has challenged Mr Heaton-Harris on the universality of the 27.5 per cent reduction for members of the crisis-hit Assembly in Belfast.
The government this week announced the change along with an extension to the deadline for a Northern Ireland executive to be formed.
The new December 8 deadline can be further extended by six weeks, meaning the latest a ballot can be held is April 13 2023.