Gibraltar's government has accused its closest neighbour of trying to use Brexit to further its longstanding claims over the British overseas territory.
Rt Rev Robert Innes from the Diocese of Europe, which has its mother church in Gibraltar (pictured below), said residents fear a return to days when there were tighter border controls.
He said: "It would be evident that there would be a customs border of some kind between Spain and Gibraltar, and whether Spain chooses to keep that border open or put big controls on it, is really at their discretion."
The plans would require Spanish agreement before Gibraltar is included in future deals concerning areas such as trade between the European Union and UK, post-Brexit.
The shadow Brexit secretary Sir Keir Starmer told ministers Gibraltar must not be used as a "bargaining chip" in negotiations surrounding the UK's exit from the European Union.
Bishop Robert (pictured below) went on to say: "For the folk in Gibraltar, this is very scary because they can remember what it's like to live with a close border with Spain and they fear those days may come back in future.
"They depend on an open border with Spain for nearly all their fresh fruit and vegetables, and for the free movement of about 10,000 workers who come in to work in the morning and leave in the evening."
Gibraltar's chief minister Fabian Picardo met with the foreign secretary on Friday, when Boris Johnson tried to reassure him of the UK's ongoing support.
Gibraltar, which is located on the southern tip of the Iberian peninsula, has been ruled by Britain for 300 years.
Meanwhile, Labour member of the European Parliament for Gibraltar, Clare Moody, said it was shocking Mrs May's Article 50 letter this week made no reference to Gibraltar.
She told BBC Radio 4's Today programme: "It is the UK Government's job to represent the people of Gibraltar, and I was amazed that they failed to do that in the letter that they sent in on Wednesday."
Bishop Robert said: "The prime minister's Article 50 letter made no mention of safeguarding the special situation of Gibraltar and that meant that the door was open in its negotiating position to include specifically its views on the future of Gibraltar."
Downing Street said Theresa May made clear in the House of Commons on Wednesday the support of the Government to the people and economy of Gibraltar was "absolutely steadfast."
Listen to Premier's Alex Williams speaking with Bishop Robert: