Brexit would cause issues for church staff working across the EU that would vary in "range and complexity", the Bishop of Europe said.
Rt Rev Robert Innes (below) told Premier he was already in discussions with senior government figures about a way forward.
"We'd like things to continue for us, just as they are at present," he said.
Pressed if he thought that was possible he replied: "Yes I do, I think that can be negotiated and I hope they will do that."
Concerns range from health care and pensions to visas and problems for families with dual nationality.
Bishop Robert said: "It was very clear that the biggest worries are over health care and pensions.
"Of course for me as a bishop, I have particular concerns that the most vulnerable people should not be placed in situations of real stress, uncertainty and possible poverty."
He told Premier that many of his staff and parishioners were "very stressed".
He said: "You can imagine if you're elderly and you've sold up in the UK, you've moved to a much cheaper property, lets say in Spain or rural France, and now you're not sure whether you will continue to have the right to reside in these countries or continue to be able to access health care, that is a scary position for an older person to be in."
The bishop warned that Brexit would affect the Church for years to come: "It creates extra complexities for recruiting.
"Currently it's very easy for us to move clergy between the UK and Europe whereas when we leave the EU we might face issues of visas and restrictions on the entry of religious workers.
"So we are concerned about that too."
The government is preparing to set it what it wants to achieve in the divorce deal from the EU in a white paper.
Prime Minister Theresa May says she will seek the best deal for the UK and the bloc group.
Listen to Premier's Antony Bushfield speaking to Rt Rev Robert Innes:
