The men were reportedly 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.
In the open letter, which has been signed by the Bishops of Willesden and Buckingham, the clergy say: "These are respected Christian leaders, whose bona fides could easily have been checked with the Archbishop of Canterbury's office at Lambeth Palace, or with the Syriac Orthodox Church in this country.
"The reasons given for the refusal of their visa applications (either that they had insufficient funds to support themselves while in the UK, or that there was reason to be concerned that they might not leave the country afterwards) do not seem to take seriously the reality of the Archbishops' urgent and serious pastoral responsibilities in their home countries.
"We entirely understand that as Secretary of State you are unable to comment on individual cases. However, when three separate applications from prominent Christian leaders are rejected on grounds where doubtless guarantees could easily have been found, there must surely be a problem with the system.
"We call on you urgently to investigate how such a state of affairs has come to exist, and to consider what reforms can be put into place to ensure a more equitable and compassionate system of assessment for such applications.
In response to reports on the visa ban, 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."