Conservative MPs are working alongside members of the controversial Alleanza Nazionale party in the Council of Europe in Strasbourg.
Alleanza Nazionale has its roots in Benito Mussolini's blackshirt Fascist movement and numbers Mussolini's granddaughter among its MPs.
The Tory group is teamed up with the Italians in the European Democratic Group in the Parliamentary Assembly of the Council, the 286-strong body that represents 40 countries across the continent.
Among the Tory MPs in the group is Sir Alastair Goodlad, Britain's new High Commissioner to Australia and Mr Hague's nominee for European Commissioner in Brussels.
The centre-right alliance is chaired by David Atkinson, MP for Bournemouth East, while one of its vice-chairmen is Giusepe Turni, an Alleanza Nazionale MP.
Mr Atkinson was nominated for the post of Tory group leader by the Chief Whip, James Arbuthnot, and approved by Mr Hague himself.
According to the website of the European Democratic Group, other Tory members include the MPs John Townend, Michael Colvin and Christopher Gill, and the former whip Lord Lucas of Crudwell. The group's auditor is Sir Sydney Chapman MP. As well as Mr Turini, there are four other Alleanza Nazionale MPs listed as members of the European Democrat Group.
The group's statute describes itself as a "centre-right coalition of colleagues" whose objectives include respect of individual liberty and support of a free market economy.
Mr Atkinson, who said that he had the approval of Mr Hague to allow Tories to join the group, said he was not embarrassed by the formal alliance with the Italian party.
"They are our colleagues in our group and there are no grounds for them not being members of our group, provided they support our aims and provided we regard them, as we do, as a democratic party in a democratic country.
"I don't see there's a problem here. They can no longer be regarded as a Fascist party."
However, Mr Hague has described Alleanza Nazionale as "neo-Fascists" and insisted that there is no question of Tory MEPs joining up with the party in Strasbourg.