Former Secretary of State Lord Peter Hain has warned that the UK leaving the European Court of Justice could compromise peace funding to Northern Ireland of around £240 million.
As it currently stands, grants totalling around that figure are paid to Northern Ireland as part of reconciliation funding.
In a statement to the BBC, Lord Hain has said that it would be "the height of irresponsibility for the Government to look a gift horse in the mouth" due to its "obsession with the ECJ".
As it stands Northern Ireland is in receipt of a funding block known as PEACE IV, which will run until 2020.
The UK's position on Brexit maintains a commitment to continue the implementation of the EU's PEACE programme, the current incarnation of which runs until 2020.
Between 1995 and 2013 the PEACE programmes have allocated just over £1.8 billion to projects supporting peace and reconciliation in Northern Ireland.
In his statement, Lord Hain said: "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 position paper on Brexit, the UK government has said that it will examine the possibility of extended the PEACE programme beyond the current 2020 end date.