Extra police have been deployed at polling stations in some parts of the country amid vote rigging fears.
Birmingham has been dogged by vote fraud allegations
West Yorkshire police say they are investigating a "small number" of vote fraud claims in Bradford.
And West Midlands police have launched an investigation in Birmingham, which saw large scale vote fraud during 2004's council elections.
Officers are keeping watch at polling stations in both areas in an effort to prevent foul play and intimidation.
Police are focusing on Birmingham's Bordesley Green ward, where "anomalies" in 190 postal votes are being studied by specialist teams.
Birmingham city council leader Mike Whitby asked for police officers to be deployed in wards considered at greatest risk from fraud and intimidation.
Mr Whitby said this would ensure the election was "free, fair and clear of any illegal or corrupt practices".
West Midlands Police said the positioning of officers at polling stations was a "fluid situation" and the force would decide throughout the day whether and where to deploy them.
Birmingham's council polls were marred by fraud in 2004, when an elections judge said the evidence he heard would "disgrace a banana republic".
So far this year, two arrests have been made.
The number of postal vote applications in Birmingham has fallen from more than 70,000 in the general election of 2005 to fewer than 60,000 this year.
However, there are increases of up to 30% in five wards.
In London, allegations of vote rigging have been made in seven of the 32 boroughs.
The Metropolitan Police said it was continuing its investigations but could not clarify whether officers would have a greater presence than normal at polling stations.
Harrow, Kensington and Chelsea, Merton, Southwark, Hounslow, Tower Hamlets and Barnet are being examined by the force's specialist operations command.
It is assessing each allegation alongside the Crown Prosecution Service, the Electoral Commission and each of the local councils involved.
Polls will remain open across England until 2200 BST with a total of 4,360 council seats being contested in 144 local authorities and the 32 London boroughs.
Approximately 23m people are eligible to vote, which is more than half of the UK's electorate.
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