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Conservative Party leader David Cameron has said a new government must ensure there is no repeat of chaotic election day scenes in which people were still queuing in their hundreds outside polling stations when the ballot boxes closed.
The Electoral Commission has pledged a "thorough review" into problems around the country, including London, Sheffield, Manchester, Liverpool and Newcastle.
Prime Minister Gordon Brown also expressed concern at the reports of queues up to two hours long and people being turned away from voting at 10pm in the face of high turnouts and low staff numbers at polling stations.
A spokesman for Gordon Brown said the Prime Minister was "very concerned by the reports and would support a thorough investigation into them".
Making his victory speech in Witney, Oxfordshire, Mr Cameron thanked local officials in his constituency for a well-run General Election day, but said that had not been the case in some parts of the country.
"An early task for a new government is to get to the bottom of what has happened and make sure that it never happens again," he said.
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The Electoral Commission said it was a cause for "serious concern" that many people who wanted to vote were prevented from doing so, and that there should have been sufficient resources allocated to make sure everyone was able to vote.
There were angry scenes at polling stations in Hackney, east London, where would-be voters staged a sit-in after they were told they could not vote, and in Lib Dem leader Nick Clegg's constituency of Sheffield Hallam, where students tried to prevent ballot boxes being taken to the count after they were turned away.
In some places, including two polling stations in Newcastle, voters were ushered into the building before 10pm when the doors had to be shut, while at one site in Lewisham, ballot papers were handed out to the queue before the deadline. But there were reports in the Manchester Withington constituency of people queuing for more than two hours before being turned away because the polls had closed.
Jenny Watson, chairwoman of the commission, said the current system was "at breaking point" and the law might need to be changed as a result of the scenes witnessed on Thursday.
