Supreme Court judges will be asked this week to rule whether five men accused of taking part in the 1994 Rwandan genocide should be extradited to face trial.

The five suspects, Vincent Bajinya, Celestin Ugirashebuja, Charles Munyaneza, Emmanuel Nteziryayo and Celestin Mutabaruka, are all charged with crimes against humanity and mass murder relating to the 100-day genocide on the Tutsi community in 1994. They were arrested in May 2013 after living in the UK for more than a decade, but are appealing against extradition on the grounds that they would not receive a fair trial in Rwanda. Their lawyers will claim that key witnesses are too afraid to give evidence in open court.

The Supreme Court ruling could have significant political ramifications. Relations between Britain and Rwanda have been warm after Britain provided support for the East African nation after the genocide. However, human rights campaigners have called for Britain to adopt a tougher attitude to President Paul Kagame's regime, following allegations of widespread abuses against his opponents.

Witnesses for the defendants at an earlier extradition hearing requested that they give their evidence to lawyers in private, which would not be disclosed to the government of Rwanda because they feared for their safety. However, Westminster magistrates who heard the extradition denied the request, concluding that excluding one party in the trial would be unlawful.

If the appeal is won, the five men will be granted permission to remain and stand trial in the UK. If the appeal is lost, however, extradition of the defendants may be in breach of the 1998 Human Rights Act, with the suspects being subjected to a "flagrantly unfair trial".

A decision was due to be heard in October last year, but was delayed due to the complex nature of the case. Mr Ugirashebuja, 60, a careworker from Walton-on-the-Naze, Essex; Mr Munyaneza, 55, from Bedford; Mr Bajinya, 52, from London; and Mr Nteziryayo, 60, a father of five from Manchester, were all previously arrested in 2006, but the trial collapsed three years later. Mr Mutabaruka, 57, from Ashord, Kent, was arrested for the first time last year. He is a pastor at a community church and has five children.

Mr Bajinya, who changed his name to Vincent Brown on becoming a British citizen in 2006, is accused of having a personal involvement in the genocide, by actions which included organising road blocks so that Tutsis could not escape being killed.

A medical doctor, he claimed asylum in the UK after the genocide and worked for a London-based charity for victims of torture. He is said to have been a militia organiser and a member of President Juvénal Habyarimana's Akazu, an informal organisation of Hutu extremists.