Police are carrying out eight investigations into allegations of electoral malpractice in a borough where counting took five days amid allegations of voter intimidation.
The Metropolitan Police said it had received 84 complaints in relation to Tower Hamlets although in the "majority of cases" there is no evidence that any criminal offences have been committed.
The eight investigations being carried out in Tower Hamlets include one allegation of failing to put a correct imprint on election literature, one of making a false statement about a candidate, four of false declarations on nomination papers and two relating to postal voting.
Officers arrested a 24-year-old man yesterday on suspicion of conspiracy t o defraud in relation to postal vote applications. He was released pending further inquiries and is due to return in mid-July.
A 38-year-old man was arrested on May 13 in Tower Hamlets on suspicion of an offence under the Representation of the People Act 1983 in connection with an allegation of potential false declarations on nomination forms.
The Electoral Commission has announced it will look into allegations of voter intimidation and the Met confirmed it had received a number of complaints related to behaviour at polling stations.
Scotland Yard said "th ese are currently being assessed in conjunction with our partners" and insisted there had been a "strong police presence" on the day of the election, with an officer at each polling station in Tower Hamlets.
As well as the eight Tower Hamlets investigations, six other cases are being examined in other areas of the capital: four allegations of false declarations on nomination papers; one allegation of bribery; and one of forgery.
After last month's elections Labour emerged as the largest party in Tower Hamlets with 20 seats, two more than the Tower Hamlets First party established by mayor Lutfur Rahman, who split from Labour in 2010.
One further ward, Blackwall and Cubitt Town, still needs to have three new councillors elected after polls were called off following the death of a candidate. The seats were won by the Conservatives at the last election but would be enough to make either Labour the majority party or Tower Hamlets First the largest group depending on the outcome.
The Met said it would put in place a "robust policing plan" for the July 3 by-election.
A council spokesman said: "We welcome the thoroughness of the police investigation into complaints about the 2014 borough elections.
"We note that whilst the police have received 84 complaints, only eight of the complaints merit an investigation as in the majority of cases there is no evidence that any criminal offences have been committed.
"Of the eight investigations, one refers to an allegation of failing to put a correct imprint on election literature, one of making a false statement about a candidate, four of false declarations on nomination papers and two relating to postal voting."
Returning officer John Williams said the local authority had "worked closely with the police to respond quickly to all allegations received in accordance with our local protocol and refer issues for investigation where necessary".
He is also looking into what the council described as " a number of complaints which, while not alleging a criminal offence, could represent a breach of the Tower Hamlets Local Protocol".
"Any concerns will be discussed with the election agents and candidates ahead of the pending Blackwall and Cubitt Town ward election," it said.