Hundreds of people were unable to vote at polling stations last night as they were still queuing when the ballot boxes closed at 10pm.
Voters in Hackney, east London, were turned away from a polling station in Triangle Road after some had been forced to queue for more than an hour and a half, they said.
And police were called to a polling station in Manwood Road, Lewisham, south London, where around 300 people had yet to vote by 10pm, Scotland Yard said.
There were reports of similar situations in other parts of the country.
In Hackney, where residents were voting for their MP, councillors and the borough's elected mayor, at least 150 people were still queuing when the polls closed, according to Andrew Boff, Conservative mayoral candidate.
He said the number who were not able to vote before the 10pm deadline could be double that figure, as some people had given up in the face of long queues - and that "it was getting ugly" after people were told they could not vote at the polling station which had just three staff.
"At 10pm the ballot boxes were closed and people were told they would not have a vote," he said.
"People were very angry."
Would-be voters staged a sit-in protest at the building after the ballot boxes closed and police had to be called.
Liz Veitch, the last person to vote at the polling station after waiting for more than an hour and a half, said the queue had been snaking out of the building and down the street.
"There are an awful lot of extremely angry people around here.
"It's an absolute scandal. I can't see how the results for Hackney can be counted as the results of the election," she said.
Voters were turned away from polling stations in Sheffield Hallam, where Liberal Democrat leader Nick Clegg was standing.
A number of voters, mainly students, were turned away after attempting to vote shortly before the 10pm deadline because they did not have polling cards, a Sheffield City Council source said.
John Mothersole, returning officer for Sheffield, apologised to residents who were unable to vote.
He said: "We got this wrong and I would like to apologise.
"We were faced with a difficult situation with the numbers of people, and a large amount of students turning up to vote without polling cards.
"This made the administration process of ensuring the correct person was given a ballot paper much longer.
"The only remedy, which we could not take, was to extend the voting times."
In Lewisham, there were reports that the polling station stayed open for half an hour beyond the 10pm deadline to allow people to vote.
Labour Party deputy leader Harriet Harman said on Sky News that when she left her Camberwell and Peckham constituency tonight, people were still queuing up outside waiting to vote.
"It shows that there has been a high turn-out. We have got to make sure that all the votes are counted."
She said that polling stations closed their doors at 10pm but those already inside could vote. These arrangements were not a matter for the Government but for the election authorities, she added.
Business Secretary Lord Mandelson acknowledged on BBC News that the situation could lead to legal challenges.
"What the returning officers should have done is brought everyone in and locked the door."
He said he was concerned about the failure of some people to get in and vote because traditionally Conservatives voted earlier than Labour supporters.
Tory party chairman Eric Pickles commented: "It's ridiculous. Of course people should be able to vote.
"Surely to goodness the returning officers could have just put the people in the polling station and continued."
Shadow business secretary Kenneth Clarke said he was "very sorry" to hear about reports of problems at some polling stations.
"It's very worrying indeed," he told Sky News. "I feel sympathy for the people who were trying to do the thing they should do, go along and cast a vote.
"I trust somebody sorts out what on earth went wrong and made it so difficult for people to vote.
"I'm obviously not going to leap to any conclusions about what went wrong in Sheffield, Manchester and Islington but the returning officers may owe people an apology if it's in any way down to them and I think we ought to get an explanation."
He added: "The Electoral Commission might prove its worth by making sure it never happens again."
A Conservative party spokesman commented: "These are very disturbing stories which clearly need to be thoroughly investigated."
ITV News showed amateur footage which the channel said was of people being turned away from a polling station in Manchester Withington.
Labour former home secretary John Reid said: "If the whole point of the television debates... is to bring more people out - provided, of course, that they arrived before the polls were due to close, and we don't know that from those films - but if they did and didn't get a chance to exercise their democratic right to vote, then that is a very bad show."
Asked if the situation amounted to a "scandal", Olympics Minister Tessa Jowell replied: "I think it is.
"These are queues of people exercising their democratic right and then being denied it."
She said the administration of elections fell to local authority returning officers and it would be important to investigate individual circumstances afterwards.
Mr Pickles demanded: "How can a polling station actually run out of ballot papers? Not to have sufficient ballot papers seems ridiculous."