Police are investigating five allegations of electoral irregularities related to the Peterborough byelection, which Labour won by 683 votes.

Three of these relate to postal votes, one allegation is of bribery and corruption and the fifth is of a breach of the privacy of the vote, Cambridgeshire police have confirmed.

The Labour candidate, Lisa Forbes, was elected after the byelection on 6 June, with Nigel Farage’s Brexit party in second place.

Postal votes accounted for 9,898 of the 33,998 ballot papers received. About 400 of the postal votes returned were rejected due to either the signature or date of birth or both not matching council records.

The byelection was called after Peterborough’s previous MP, Fiona Onasanya, was forced out after she was jailed for lying about a speeding offence. Onasanya was elected as a Labour MP in 2017 with a wafer-thin majority of 607, but was suspended from the party after she was sentenced.

On election night, Brexit party sources were briefing that they believed that there were irregularities surrounding the city’s Asian community. Farage went further on Sunday by calling Peterborough a “rotten borough” – and blaming the postal vote system for his party’s loss.

He told MailOnline: “I think there is something inherently wrong with the entire postal voting process in this country. I think it’s open to corruption, bribery intimidation, abuse. We’ve seen so many cases now where again and again we find – particularly in the inner cities – postal voting is producing the wrong results.

“And I’m afraid Peterborough looks like another one of those rotten boroughs.”

Peterborough council said on 10 June that it received one unconfirmed report regarding alleged bribery before polling day. This was referred to the police and no further action would be taken, the authority said.

Police have been asked to investigate a claim, made on social media, that an individual burned more than 1,000 votes destined for the Brexit party; and that some voters were observed taking photographs of ballot papers, leading to concerns that they were fulfilling some form of contract.

It is not known if these claims are part of the latest Cambridgeshire police inquiry.

In a statement, the council said that on top of the claims sent to the police, another concern was received on polling day that was also referred to police, but could not be substantiated.

The council said it had seen no evidence postal voting fraud had taken place.

Labour sources have previously said claims that their campaigners have been involved in electoral fraud are a “racist trope”.