The East London borough has been in the spotlight since Rahman's re-election amid allegations of voter intimidation and fraud.
Controversial Tower Hamlets mayor Lutfur Rahman has been told to expect "proper scrutiny" following the results of a by-election.
Voting has begun in Tower Hamlets' Blackwall and Cubitt Town by-election.
Tower Hamlets returning officer John Williams says more police will be at polling stations to stop fraud.
At least six police officers will be on duty at each of the polling stations.
Councillor Peter Golds said: "I want to see the police ensure that anyone can enter a polling station without hindrance from groups of people trying to canvass them as they try to go in."
He added: "I also want the police to ensure that when people are inside the polling stations voters vote unhindered and people are allowed to cast their vote in private."
Tower Hamlets Tory leader Peter Golds is demanding police action to prevent intimidation at Thursday's by-election. Three seats are being contested by 21 candidates in Blackwall and Cubitt Town ward.
The Electoral Commission has ordered the council to avoid a repeat of May's election count fiasco.
A senior civil servant has complained of delays in the release of information by Tower Hamlets during an official investigation. Communities Secretary Eric Pickles ordered a probe into alleged poor financial management and fraud in April.
Inspectors from PricewaterhouseCoopers were due to report today but have been given more time. The civil servant says information material to inspection made available "only after delay or not at all".
Labour has denied claims there are plans to readmit Lutfur Rahman to the party. The controversial Mayor of Tower Hamlets founded the Tower Hamlets First party last year having left the Labour Party in 2010 and standing as an independent ever since.
– Metropolitan Police
Officers from the Specialist Crime and Operations Directorate have received a total of 84 complaints of electoral malpractice in relation to the borough of Tower Hamlets.
Following a thorough assessment of all complaints, it has been determined that in the majority of cases there is no evidence that any criminal offences have been committed.
A number of complaints received relate to alleged behaviour of campaigners at polling stations in Tower Hamlets on 22 May and these are currently being assessed in conjunction with our partners.
Boris Johnson on Tower Hamlets election "everybody had been a bit concerned about irregularities frankly in the voting." @itvlondon
Johnson: I am concerned. I know the police are looking at a lot of stuff at the moment. @itvlondon
London mayor Boris Johnson says police briefed him about a high volume of complaints of alleged vote-rigging in Tower Hamlets. @itvlondon