The remaining 27 EU countries are set to rubber-stamp negotiating guidelines from the EU President Donald Tusk at a European Council summit on April 29.
"Our countries are potentially among the countries which will be most affected by the Brexit," Denmark's prime minister Lars Løkke Rasmussen told a joint press conference.
"We need to reduce the damages of Brexit as much as possible and build a new working relationship."
Denmark, Ireland and The Netherlands are all heavily dependent on trade with Britain.
Dutch Prime Minister Mark Rutte said the EU needed to "act in concert" during the Brexit negotiations, saying "unity" was in everyone's best interests.
"We will need to have as 27 countries a unified position with one negotiator working on behalf of all of us," he said, after talks in The Hague with Irish Prime Minister Enda Kenny and his Danish counterpart Rasmussen.
A Dutch government think-tank warned last year before Britain's referendum that Brexit could cost The Netherlands a 1.2-percent fall in GDP by 2030 and a 10-billion-euro trade loss.
Given the extent of trade between our three countries and the United Kingdom, it's very important that there will be clarity and movement to those issues as soon as it's appropriate," said Kenny.
"We want to minimise any major impact to our economy as with the Netherlands and Denmark."
Rutte stressed that some of the burning issues were the status of EU citizens living in Britain, as well as European business located there, Britain's potential Brexit "bill" and the issue of borders.
Kenny, who recently met the Spanish, Polish, Belgian and German leaders, said: "We want to protect jobs, we want to grow jobs and increase prosperity.
"We want to provide as much clarity and certainty for businesses from our three countries about trade with United Kingdom," he added.
Ireland is also particularly concerned by the borders question as it shares a land border with Britain to its north.
But Kenny highlighted: "The agenda of the European Union is beyond Brexit... with opportunities for expansion, job creation, investment and above all continued peace, and that should not be derailed by the Brexit negotiations."