Gosport Borough Council has said 44 people were unable to vote yesterday because they did not bring the necessary ID.
The borough was one of five areas trialling a system to help stop electoral fraud.
Residents were required to show photo ID such as a passport or driving licence, or two non-photo items such as a council tax bill and bank statement.
The borough said 20,612 people voted, including 72 people who returned with ID after initially being turned away at polling stations.
Returning Officer Michael Lawther said: "We ran a very extensive publicity campaign to tell people they needed to bring ID, and what types of ID were acceptable."