The Fianna Fáil leader has said the government needs to use all its influence to convince the UK to remain in the EU customs union.
Micheál Martin said the nature of trade between Ireland and the UK following Brexit is critical to the future of both islands.
The third round of negotiations between the UK and the EU will get underway in Brussels later.
The talks are resuming against the backdrop of a dramatic shift in policy from the Labour Party in Britain - which has announced it would keep the UK inside the EU's single market and customs union during a transition period expected to last as long as four years following the official date for Brexit in 2019.
Deputy Martin welcomed the change – adding that a British exit from the customs union could have “very dire” implications for Ireland.
“I don’t think people have faced up to that reality and I think more effort and more energy has to be put in to understanding the dynamics of British politics at the moment and using what influence we have to seek to direct the debate towards a more sensible outcome for Britain, for Ireland and indeed for Europe,” he said.
"Flexibility and imagination"
Britain’s Secretary of State for Exiting the European Union, David Davis has called on the EU to demonstrate "flexibility and imagination" as the latest round of talks gets underway in Brussels.
The Brexit Secretary has called for the negotiations to be broadened beyond the divorce itself - and to include future trade relations.
While both sides accept progress has been made on the issues of citizens' rights, the Irish border and the "divorce bill," the European Union has warned that not enough has been achieved.
Chief EU negotiator Michel Barnier, is understood to be infuriated at Britain's refusal to spell out how it thinks its liabilities to the EU should be calculated - let alone put a figure on the final bill.
Britain has accused Brussels of "massively over-egging" its financial demands, which have been estimated at between £50 - £80bn (€54 - €86bn).
The EU has also accused the UK of "magical thinking" on its solutions to providing a frictionless border in Ireland.
But Mr Davis hopes the series of papers produced by his Department for Exiting the EU over the past fortnight demonstrate that the divorce from the EU is inextricably linked to the future relationship between the two sides.
He is expected to say he wants to agree a deal which is in the best interests of both sides, and expects the four days of talks to be "constructive."
"For the UK, the week ahead is about driving forward the technical discussions across all the issues.
"We want to lock in the points where we agree, unpick the areas where we disagree, and make further progress on a range of issues.
"But in order to do that, we'll require flexibility and imagination from both sides."
He will add: "Our goal remains the same. We want to agree a deal that works in the best interests of both the EU and the UK, and people and businesses right across Europe.
"And we're ready to roll up our sleeves and get down to work once more."
The Conservative Party has accused Labour of "a weak attempt to kick the can down the road," following its announcement that it would keep the UK inside the single market and customs union during a four-year transition period.
Labour's plans would mean the UK observing EU rules allowing free movement of people and barring trade talks with non-EU states during this period.
The party’s leader Jeremy Corbyn said “confusion” over policy had left Mr Davis "in danger of wandering into a cliff-edge Brexit" in the Brussels talks.