Two prominent Saudi princes are involved in a London-registered company that supposedly facilitated "money laundering" for Hezbollah in Lebanon and helped smuggle precious stones out of Congo, according to contested allegations in court documents obtained by the Guardian.

The claims emerge from court papers that lawyers for the Saudis have spent a year trying to suppress, including resorting to threats that relations with Britain would be damaged if they were revealed.

Lawyers for the two princes – Prince Mishal bin Abdulaziz Al Saud, a former defence minister, brother of King Abdullah and chairman of the country's influential allegiance council, and his son Prince Abdulaziz bin Mishal bin Al Saud – dismiss the claims as fabrications, "extortion" and "blackmail".

They contend that their former partner, a Jordanian, Faisal Almhairat, "misappropriated" money from accounts, denied them access to company books, shut down the shared business and "interfered with the negotiations" on telecommunications deals. Almhairat, in turn, disputes their claims.

In the context of Middle East politics, the suggestion that two prominent Sunni Muslims from the Saudi royal family have been surreptitiously dealing for profit with Hezbollah, a Shia force supported by Iran, is extremely damaging. Hezbollah is designated a terrorist organisation by the US.

The Guardian and Financial Times originally requested to see the court documents – filed as part of a commercial dispute between Almhairat and the Saudis – in spring 2012. On Thursday, the court of appeal finally agreed to the immediate release of the statements of case.

Among other allegations is the claim that at the "instigation" of Prince Abdulaziz, Saudi police issued an arrest warrant for Almhairat and asked Interpol to issue a red notice sanctioning the extradition of the Saudis' former business partner to Saudi Arabia.

The case revolves around a catastrophic breakdown in relations between Almhairat and the Saudis. They were business partners in a London registered telecommunications company, Fi Call Ltd, whose capital value was £300m.

Fi Call was developing a software application for smartphones that would allow users to make free phone calls. The Saudis' shares were mainly held through Global Torch Ltd, a British Virgin Islands company that the princes are said by Almhairat to control. Almhairat's shares are held by his Seychelles-based firm Apex Global Management.

The dispute, which erupted over allegedly misappropriated money and the sale of $6.7m (£4.3m) worth of shares, has "thrown up a nuclear mushroom cloud" of litigation, according to Mr Justice Morgan, who gave judgment at an early stage in the litigation.

The case raises questions about whether the transparency of British justice can be upheld at a time when the Ministry of Justice is eagerly inviting wealthy, international claimants to resolve their disputes in London's commercial courts.

The legal dispute was initiated by Global Torch but a counter-petition by Almhairat forced the two Saudi princes to become involved in the case. The princes then tried unsuccessfully to extract themselves from the proceedings by claiming "sovereign immunity". Prince Mishal is aged 86 and said to be in frail health.

A further, preliminary hearing is due to take place next week at the Rolls Building in central London where commercial disputes are tried. That argument will focus on an application by the princes that the UK courts do not have jurisdiction to involve them in the counter-claim launched by Apex and Almhairat.

The full trial, if it goes ahead, is due to be heard in January next year. On Thursday three judges in the court of appeal, Lord Justice Kay, Lord Justice Richards and Lord Justice Briggs, lifted a stay on reporting court submissions. They are due to give their reasoning at a later date.

None of the factual issues have yet been resolved by the court. The allegations are fiercely contested on both sides. At one point in a court document, lawyers for Almhairat remark: "Each side maintains that the other is lying about almost everything."

During the appeal court hearing, Guy Vassall-Adams, counsel for the Guardian and Financial Times, said: "Global Torch has chosen to bring proceedings in this jurisdiction. This is an open justice jurisdiction.

"They [the Saudis] have to accept that these damaging allegations will be heard in open court in the usual way. The protection they are entitled to is a judgment delivered in public which will refute unfounded allegations. That's how a legal system works in a democracy under the rule of law."

The case continues.