The men were told they would not be allowed to come to Britain in case they did not return to the war-torn region. One clergyman was told it was against UK Government policy to grant a Syrian a visa.
Archbishop of Mosul Nicodemus Daoud Sharaf, Archbishop of St Matthew's Diocese Timothius Mousa Shamani and Archbishop Selwanos Boutros Alnemeh of Homs in Syria were due to visit the UK at the end of November.
They were coming to attend the consecration of the UK's first Syriac Orthodox Cathedral, which was attended by Prince Charles.
One critic was quoted by the Daily Express as saying that Muslim clerics had been granted visas to come to the UK.
A Home Office spokesperson said: "All visa applications are considered on their individual merits and applicants must provide evidence to show they meet the requirements of the immigration rules."
