Despite the rain, temporary booths were set up outside in the car park of the polling station at Christ Church, in Quay Road.
Some voters were asked to mark their ballot paper from the back of a car while others were asked to rest on one of the nearby dustbins.
A Bridlington resident said she arrived at the polling station after 7am and couldn't believe it was being held in the car park.
She said: "They had two dustbins to rest on. There's no privacy, the slips are getting damaged and wet.
"No one is letting them in the church. People are just walking away."
One Bridlington voter tweeted that he had to vote out the back of a car when he arrived at 7.10am this morning (Thursday June 8).
The polling station is now open.
A spokesperson for the East Riding of Yorkshire Council said: "There was a delay at the polling station opening at Christ Church in Bridlington. Council officers acted in accordance with the guidance set op by the electoral commission and polling booths were set up in the car park. We are now in the building."