In what the families’ lawyers described as "a stunning victory", the Court of Appeal ruled that they were entitled to seek a judicial review of the Government’s refusal to hold an inquiry into why Britain entered the conflict.

The three appeal judges headed by the Master of the Rolls, Sir Anthony Clarke, concluded that there was "force" in the argument that the circumstances leading up to the invasion were insufficiently clear as to warrant investigation, as did the lawfulness of the invasion itself and whether it caused the men’s deaths.

The applicants are relatives of four servicemen who died in military action between 2003 and 2005 who are seeking to force a full public inquiry into why Britain entered the conflict.

A three-day hearing - effectively a full hearing of the arguments - is scheduled for November.

But the judges warned that although they had granted permission, they saw "formidable hurdles in the way of the applicants and do not wish to encourage them to think that they will succeed."

The judges added: "We are doubtful whether it would be appropriate to order a public inquiry of the kind sought."

The application for judicial review was "unpromising". The matters raised were "essentially matters for the executive and Parliament".

But permission was being granted "because the case raises questions of considerable general importance which should, we think, be finally decided after full argument".

Lawyers for the Prime Minister will now have to submit detailed evidence in support of their argument that a public inquiry is not required.

This morning’s ruling was given by a panel of top judges - Sir Anthony Clarke; the President of the Queen’s Bench Division of the High Court Lord Justice Judge, and Lord Justice Dyson.

The full hearing will take place before the same judges over two or three days, beginning on November 6.

Despite the judges’ warning on the families’ prospects of success, their solicitor, Phil Shiner, described the go-ahead as "a stunning victory" which would force the Government to put evidence before the judges on how the country was taken to war.

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