Lord Peter Hain has called on the government to "soften" its approach to "taking the UK out of the jurisdiction of the European Court of Justice (ECJ)."
The former secretary of state claimed that such a move could result in Northern Ireland losing millions of pounds of peace funding.
The ECJ oversees reconciliation grants to NI in the region of £240m.
The current funding block, known as Peace IV, runs until 2020.
In the UK Brexit position paper, the government pledged its commitment to maintaining the "implementation of the Peace IV programme."
However Lord Hain said if this was the case, the government should reconsider its "dogmatic insistence" on removing the UK from the ECJ.
In a statement, he said: "The EU's PEACE programme has made a massive contribution to helping communities across Northern Ireland put the past behind them and build a brighter, more cohesive future.
"Michel Barnier has been clear that he values the EU's work on the peace process and wants to see it continued.
"It would be the height of irresponsibility for the Government to look a gift horse in the mouth and give that funding up because of their obsession with the ECJ.
Lord Hain added: "Ministers themselves say the UK should remain part of the PEACE Programme. But they have not faced up to the reality that this cannot be squared with their policy of leaving the jurisdiction of the ECJ.
"The Government needs to bow to reality and accept that this programme will require the softening of their unnecessary red line on judicial sovereignty."
In its Brexit position paper the UK government said: "The UK proposes that, without prejudice to the wider discussions on the financial settlement and Structural and Investment Funds, the UK and the EU should agree the continuation of funding for PEACE IV for the duration of the existing programme and with the Northern Ireland Executive and Irish Government, explore a potential future programme post-2020.
"In doing so, the UK wants to work with the EU on how together we can maintain the implementation of the PEACE IV programme, including the role of the SEUPB as managing authority13, and that of the NSMC in agreeing the policy direction of future programmes.
"Notwithstanding the outcome of the negotiations on this specific issue, the UK government would remain committed to peace and reconciliation programmes and to sustaining cross-border cooperation."