Finance ministers in Northern Ireland, Scotland and Wales have called for a cash injection in the Government's autumn statement, to be released next month.
Austerity should be eased as the UK gears up to deal with Brexit, the politicians warned central government.
Stormont's Mairtin O Muilleoir, Holyrood's Derek Mackay and Mark Drakeford from Cardiff are to meet Chief Secretary to the Treasury David Gauke on Monday, after the three ministers held talks in Newry yesterday.
Mr O Muilleoir said: "There is an opportunity for (Chancellor) Philip Hammond on the 23rd of November to take his foot off the austerity pedal in terms of our resource budget and our budget for services.
"We will be saying very firmly to him - and already have been - that there needs to be a real injection of capital stimulus into all the economies.
"We need the type of investment in jobs and in infrastructure that will make us economically competitive.
"The British have been focused on cuts. Heretofore I think they realise that that does not stimulate the economy, and I hope that on the 23rd of November he listens to what we have been saying, and we will be writing to him from this meeting, saying that needs to be a priority - a fiscal stimulus on the 23rd of November."
Mr Mackay said there was consensus on the impact exiting the European single market would have on GDP, employment and growth.
"The devolved administrations' finance ministers do not want to see people punished as a consequence of the mess that the Tory party has gotten us into, the hard-right Brexiteers," he added. "What we have agreed on is we want to protect our budgets and our services for the people that we represent, and we don't want to see our settlements unpicked.
"We want to see a positive fiscal stimulus to support our economy in these challenging and turbulent times."
Wales voted narrowly in favour of leaving the EU, while Northern Ireland and Scotland went the opposite way in the June 23 referendum.
But Mr Drakeford said the Welsh people did not vote to become impoverished or have their future compromised.
He added: "They would have relied on the promises that were made to them that every penny that Wales gets from Europe will come to Wales after Brexit and that a shiny future remains in prospect for people.
"So, we have agreed today on some very important common points that we will want to put in the discussions that will happen in Westminster starting on Monday and continuing after that, and where we have common ground we recognise that our voice will be stronger as a result."