It has been claimed that as 1.6m EU citizens in the UK may have been denied the vote in the European parliamentary elections on 23 May as a result of complex registration procedures.
Tens of thousands of Britons abroad are also feared to have missed out due to the late arrival of postal ballots.
Now, 37 MEPs have written to the Venice Commission asking for a formal investigation into the affair.
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They include senior Socialist members Claude Moraes and Richard Corbett as well as Greens deputy Molly Scott Cato.
The Venice Commission is an advisory body of the Council of Europe composed of independent experts in the field of constitutional law.
It was created in 1990 after the fall of the Berlin Wall when there was an urgent need for constitutional assistance in Central and Eastern Europe.
The Commission's official name is the European Commission for Democracy through Law, but due to its meeting place in Venice where sessions take place four times a year, it is usually referred to as the Venice Commission.
The body normally carries out probes into alleged corruption and vote rigging in eastern and central European countries.
“These instances where the UK has not met adequate democratic standards form part of a picture of a democracy under pressure and we are not convinced that our existing government has either the will or the capacity to address these issues”
The MEP letter was sent to Olivier Kask, who chairs the Council for Democratic Elections at the Venice Commission.
It says there was a “disenfranchisement” of non-UK EU citizens due to the “two-step process for registration in the UK.”
The letter, seen by this magazine, says UK citizens resident in other EU countries were equally disenfranchised because their postal votes did not arrive on time.
It also says there was a “breach of spending rules and data protection laws” during the EU Referendum in the UK in 2016.
“These instances where the UK has not met adequate democratic standards form part of a picture of a democracy under pressure and we are not convinced that our existing government has either the will or the capacity to address these issues.”
“We would appeal to you to offer your legal expertise in support of our democratic standards and to undertake an investigation into these issues.”
"The revelations are a major embarrassment for Britain's crisis-ridden Conservative government, as they demonstrate quite clearly that it could have easily taken steps to avoid so many EU citizens being disenfranchised” Roger Casale, New Europeans
The letter goes on to say that the MEPs who signed it “have for some time had concerns about declining democratic standards in our own country and we believe an intervention by the Venice Commission would be timely and supportive.”
“Our concerns are wide ranging and involve the exclusion of specific groups of voters and an increasing sense that both the Referendum and European elections did not reach the standards we would expect from a well-established democracy.”
Evidence about the voting affair – researched and assembled by the continent-wide campaign group New Europeans – is now being assessed by the European Parliament's Brexit Steering Group.
Roger Casale, of New Europeans, said, “Even allowing for the fact that some EU citizens may have chosen to vote in their country of origin rather than in the UK, the scale of the vote denied scandal is staggering.”
According to Casale, New Europeans found a similar level of disenfranchisement following the European elections in 2014, in which just under one million votes were denied.
"The revelations are a major embarrassment for Britain's crisis-ridden Conservative government, as they demonstrate quite clearly that it could have easily taken steps to avoid so many EU citizens being disenfranchised.”