The families of British soldiers killed in Iraq won a dramatic legal breakthrough today in their bid to force a full public inquiry into why Britain entered the conflict.

In what their lawyers described as "a stunning victory", the Court of Appeal ruled they were entitled to apply for judicial review of the Government's refusal to hold an independent inquiry.

The applicants are relatives of four servicemen who died in military action between 2003 and 2005.

But the judges warned them: "We stress that, although we have decided to grant permission, we see formidable hurdles in the way of the applicants and do not wish to encourage them to think that they will succeed."

The judges said: "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 to appeal was being granted "because the case raises questions of considerable general importance which should, we think, be finally decided after full argument".

Today's ruling was given by a panel of top judges - Master of the Rolls 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, nevertheless 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.

Mr Shiner said: "That evidence needs to establish once and for all whether the decision to invade was lawful.

"In particular, the Government must finally explain how the 13-page equivocal advice from the Attorney General of March 7, 2003 was changed within 10 days to a one-page completely unequivocal advice that an invasion would be legal.

"My clients believe he impermissibly changed his advice because he was sat on by the Prime Minister and others in Government.

"In changing his advice, he sent these soldiers to their deaths."

Today's action was brought by Peter Brierley, the father of Shaun Brierley; Beverley Clarke, the mother of David Clarke; Rose Gentle, the mother of Gordon Gentle, and Susan Smith, the mother of Phillip Hewett.

Father of one Lance Corporal Shaun Brierley, 28, whose family are from Batley, West Yorkshire, was serving with 212 Signals Squadron when he was killed in a crash in Kuwait in March 2003.

Trooper David Jeffrey Clarke, 19, from Littleworth, Staffordshire, was one of two soldiers who died in March 2003 in a "friendly fire" incident west of Basra.

Fusilier Gordon Gentle, 19, from Glasgow, of Royal Highland Fusiliers, died in June 2004 in an improvised explosive device attack on British vehicles in Basra.

Private Phillip Hewett, 21, from Tamworth, Staffs, was one of three soldiers from C Company, the 1st Battalion Staffordshire Regiment, who died in a roadside bomb blast in the Risaala district of Al Amarah in July 2005.

Peter Brierley said after today's ruling: "At last our case will be heard in full. I feel completely vindicated in bringing this case so far without any financial support.

"I am convinced that my son died for no good reason as he should not have been sent to Iraq in the first place. I am looking forward to hearing the three defendants having to explain how they justify the invasion."

Rose Gentle said: "My son died when a roadside bomb went off under the vehicle he was travelling in.

"He was in Iraq to fight for his country but I now know he should never have been sent there. He died for nothing.

"I have done everything in my power to persuade Tony Blair to meet with me but he refuses.

"Now I will finally get to see the Government have to justify their decision to invade Iraq, which most of the public believe was unlawful and counter-productive."

The appeal judges said the families' case was that the UK had an implied obligation to hold an independent inquiry into the circumstances which led to the Iraq invasion under Article 2 of the European Convention of Human Rights, which protects the "right to life".

Rabinder Singh QC, appearing for the families, had argued that the proposed investigation was not to try to make a political point but - in the words of law lord Lord Bingham - to discover the full facts in order to expose any "culpable and discreditable conduct", also to "allay suspicion of deliberate wrongdoing, if unjustified", rectify dangerous practices and procedures and give relatives of those who had lost their lives the satisfaction "of knowing that lessons learned from his death may save the lives of others".

The judges said that, since Mr Justice Collins had refused permission for judicial review, "certain information has come to light under the Freedom of Information Act.

"In the light of all the information at present available, it seems to us that, if it is otherwise appropriate to hold an inquiry, it is at least arguable that the question whether the invasion was lawful - or reasonably thought to have been lawful - as a matter of international law is worthy of investigation."

Mr Singh had argued that, in order to justify an inquiry, it was not necessary to show that the invasion was carried out in bad faith. It was enough if there was merely evidence "to suggest that the circumstances leading up to the invasion remain unclear and deserve investigation - as does the lawfulness of the invasion, and the question whether the unlawfulness of the invasion was causative of the deaths".

The judges said: "We have reached the conclusion that there is some force in those submissions."

Philip Sales, appearing for the Government, had argued that case law showed there were well-established rules that the courts would be "very slow" to intervene in matters involving sovereign states and international law, which were matters for Parliament.

The judges said Mr Sales contended that similar considerations also lead to the conclusion that it would not be appropriate to order an inquiry of the kind sought by the families.

The judges ruled: "Nevertheless, the question whether an inquiry should be ordered into the lawfulness of the invasion depends upon the true ambit of Article 2 and is therefore of some considerable importance."