Nazanin Zaghari-Ratcliffe asked to move for health reasons - but her family have raised concerns that she is being mistreated due to the ward being under the control of Iranian armed forces.
Her father tried to visit her in hospital on Tuesday but was repeatedly denied access.
Tensions have continued to grow between Britain and Iran following the recent seizing of an Iranian oil tanker off the coast of Gibraltar.
Reverend Lazarus Yeghnazar, President of 222 Ministries - a Christian organisation serving Farsi speakers in Iran told Premier the mistreatment of Nazanin by the Revolutionary Guard is sending a message to the UK government.
"The Revolutionary Guards who are virtually in control of every part of the government, their way of a dialogue is a forced reaction to certain incidents and I think they're using poor Nazanin as a pawn in their hand so that they can release their tanker which is stuck in Gibraltar."
Ms Zaghari-Ratcliffe was sentenced to five years in prison in 2016 after being accused of spying - a charge she has denied.
Both her and her husband, Richard, simultaneously protested in the form of a hunger strike against her detention and the UK has granted her diplomatic status, but Rev Lazarus thinks further action needs to be taken.
He said: "I think the West is not having a collective approach to the situation, there are many people in prison in Iran.
"The West has got to have a united front to ask them to release these prisoners, this is inhuman to use human beings as pawns for state to state discussion. It shows weakness for the Iranian government and it shows also an un-united front and attitude in Europe, which is not constructive."
He explained that it's important for the church to unite in praying for change in the region: "United prayer, of all the churches of all the Christians, unlocks many locks in Iran. I would encourage every listener to pray for the healing of the land and also the healing of the eyes of the Ayatollahs. As Christians, we forgive those who trespass against us, torture us and kill us, but God can touch their hearts as God touched the eyes of Paul and the scales fell down.
"We need to pray for the Ayatollahs, that God would show his mercy and touch their hearts."
He added: "Thousands upon thousands every month see Christ in Iran and commit their lives to Christ. Right now we have over 1000 people, being discipled and made ready for baptism. God is touching thousands of people and opening their hearts for the gospel. Why wouldn't we believe that God can touch the heart of the Ayatollahs? It seems impossible but it is possible."
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