Counts in at least 14 constituencies in eight cities including London, Sheffield and Birmingham were affected by the chaos.
People formed long lines outside polling stations as returning officers were overwhelmed by the number of people wanting to vote.
In some cases they were turned away after queuing for hours. In other cases returning officers kept the polling booths open, in contravention to election rules.
Civil rights campaigners said the scenes were “unworthy of a mature democracy like ours” and urged people to take legal action..
Geoffrey Robertson QC, a human rights lawyer, said people could get as much as £750 each in compensation for being denied the right to vote under European Law. He said: “They were terribly disappointed, they should all sue.”
Another route was for voters to club together and sue the individual council returning officers who were overseeing the chaos. This would not result in compensation for indvidual voters, however.
Under the 1983 Representation of the People Act, people would have to prove that they lost their right to vote because of a substantial failure to oversee the election.
Any hearing would be heard by two high court judges, who would be entitled to order a new by-election in the affected constituency and fine the returning officer.
These kinds of challenges to Parliamentary elections, which require a payment of £5,000 before starting the action, are extremely rare.
Liberty, the civil rights group, urged voters who were adversely affected by the problems to contact it “with a view to further action”.
Shami Chakrabarti, director of Liberty, said: “Liberty will use all legal and campaigning means to ensure that this disgrace is never repeated.”
Harriet Harman, the Labour Party deputy leader, said it was likely that several constituency results would be open to legal challenge.
At least 14 constituencies in Chester, Manchester, Leeds, Bristol, London, Sheffield, , Newcastle and Birmingham, Chester were hit.
In the Chester, where Labour’s Toby Perkins scraped in with a 549 majority, hundreds of people were reportedly turned away because polling lists had not been updated.
The Electoral Commission, which oversees the electoral system, said it would be “undertaking a thorough review of what has happened in those constituencies where people have been unable to vote”.
David Cameron, the Tory leader, said he would “get to the bottom of what has happened and make sure that never ever happens again”.