See the statement by Elizabeth Truss MP (Secretary of State for Foreign and Commonwealth Affairs).
Their release was reported by The Times 16 March 2022 - The Times view on Nazanin Zaghari-Ratcliffe’s release: Freed from Iran | Comment | The Times - where it argued that the release of "British hostages in Iran is joyful news but owes little to British or American diplomacy ..."
There is a complicated linkage between the holding by Iran of hostages and a debt owed by the UK to Iran. The debt dates back to payment in the 1970s by Iran for Chieftain tanks which were never actually delivered.
Arbitration and litigation:
The UK and Iran went toarbitration by the International Chamber of Commerce over the matter and, in 2001, an award was made in favour of Iran. An appeal was heard by the Dutch Court of Appeal where it the award was reduced. An appeal to the Dutch Supreme Court was rejected.
Iran sought enforcement of the award by applying to the High Court of England and Wales.
A further complication arose when, in 2008, the European Union added the Iranian Ministry of Defence and Armed Services to a sanctions list. The UK government then claimed that it was barred from paying the money owed.
Litigation took place in the High Court over the amount (quantum) that would be payable but for the sanction - Ministry of Defence & Support for Armed Forces of the Islamic Republic of Iran v International Military Services Ltd  EWHC 1994 (Comm) (24 July 2019) (bailii.org)
In his judgment, Phillips J noted that, due to an intervention by The Times, the hearing and the judgment were in public for reasons he gave in an earlier judgment.
The judgment of Phillips J was appealed - Ministry of Defence & Support for Armed Forces of the Islamic Republic of Iran v International Military Services Ltd  EWCA Civ 145 (12 February 2020) (bailii.org)
The issue on the appeal was the liability of the respondent, International Military Services Limited ("IMS"), for interest on sums which an arbitral panel has found to be due to the appellant, Ministry of Defence & Support for Armed Forces of the Islamic Republic of Iran ("MODSAF").
17 March 2022