The government is being urged to change polling rules to ensure voters are not turned away in their hundreds again, as happened at the general election.
Labour MP Meg Munn said the problems, experienced in Sheffield, Manchester and London and other areas, were caused by staff being overstretched.
People at some polling stations were barred from voting when queues did not clear by the 2200 BST deadline.
But the government said only about 1,200 people had been affected.
Speaking in a Westminster debate, Ms Munn, MP for Sheffield Heeley, said some polling station staff had been "simply unable to cope with the demand".
General election voters have until 0700 until 2200 to cast a ballot.
Ms Munn said: "The amount of voting hours is generous... But the rules of voting are restrictive."
Changing the rules to allow more flexibility where people are still queuing after the deadline should be "relatively straightforward", she added.
Ms Munn argued that, while the rules said there should be one presiding officer for every 2,000 voters, the figure was often more like 3,000.
Local authorities should keep better electoral records to ensure this did not happen, she said.
In addition, to enable more flexibility, there was scope for trialling weekend voting, to ensure the process was less rushed.
In response, Cabinet Office minister Mark Harper said: "There were problems at 27 polling stations out of the 40,000.
"The Electoral Commission's estimate was that the issue affected about 1,200 of the 29 million voters. Most of the 40,000 polling stations worked well."
But Mr Harper promised to keep trying to improve the system ahead of the next general election.