Police have arrested a man accused of making threats against the Labour deputy leader, Angela Rayner.

Sources close to Rayner, who is away from parliament on bereavement leave, confirmed she was the women concerned after Greater Manchester police announced the arrest.

The Guardian understands Rayner has cancelled her constituency surgeries in recent weeks amid concerns for her safety – linked to a wider increase of abuse and threats, including death threats, against her.

Friends said she had been deeply affected by the abuse, which had been taken particularly hard by her children. One described the deputy leader as “not in a good place” and said she had been unable to make many public appearances because of fears for her safety.

The force said it was investigating multiple threatening and abusive phone calls, emails and letters over recent weeks. A 52-year-old from Halifax has been arrested on suspicion of malicious communications and has since been released on bail pending further enquiries.

In a tweet, Rayner thanked the police for “supporting me, my family and my staff during this time, which has been particularly difficult for my children”.

Her spokesperson said abuse and threats had increased in recent weeks. “Angela and her staff have received a number of threatening, malicious and abusive communications in recent weeks,” the spokesperson said. “We are working with the police to ensure that the perpetrators of these crimes are brought to justice and Angela would like to thank the police for their work during these investigations.”

The spokesperson added: “Abuse and threats of this nature don’t just have an impact on Angela but also on her family, her children and her staff, who are on the receiving end of these communications.

“Angela is currently on bereavement leave after losing a close loved one and she looks forward to being back at work as soon as possible.”

DS Christopher Dean of GMP’s Tameside district said: “Abusive, threatening or bullying behaviour towards anyone is completely unacceptable and we will always do what we can to ensure those responsible are identified and held accountable for their behaviour. Although we have arrested one man our investigation very much remains ongoing and we will continue to pursue all available lines of inquiry to identify all those responsible.”

Rayner was unable to cover for Keir Starmer at prime minister’s questions – after the Labour leader tested positive for Covid – because of the bereavement, her spokesperson said.

Friends said they had had wider concerns for her safety for some time. Unlike Starmer, who has police protection, Rayner does not have her own security and staff had previously expressed concern about her travelling alone on public transport, owing to the volume of threats she had received.

One source close to Rayner in Westminster said the deputy leader had been unable to undertake many public engagements since the Labour conference. She was embroiled in a controversy at a fringe event where she described the Conservatives as “scum”.

Rayner has not held a constituency surgery in person for a number of weeks, the Guardian understands. Earlier this month, the Conservative MP Sir David Amess was stabbed to death at a constituency surgery, which led to demands in parliament for MPs to have better security and for police to take threats against them more seriously.

Amess’s death came just over five years after the Labour MP Jo Cox was murdered by a rightwing terrorist. Dozens of other MPs have seen people prosecuted for making threats against them. A neo-Nazi was jailed in May 2019 for a plot to kill the Labour MP Rosie Cooper and a female police officer.

Another man was jailed in 2018 for threats against Labour’s Diane Abbott, including threats to kill her and burn down her house.

Last year a man was jailed for sending threatening messages about another Labour MP, Yvette Cooper, and given a 10-year restraining order preventing him from contacting her or her former office manager Jade Botterill.

After Amess’s death, the home secretary, Priti Patel, announced that the threat level against MPs had been raised to “substantial”, with police saying they would work with MPs to review the security they received.

Patel urged MPs to take the “change in risk seriously” following a review by the Joint Terrorism Analysis Centre.