Benjamin Iliffe, 36, of Chatteris in Cambridgeshire, has been charged with malicious communications and possession of cannabis as part of the ongoing probe.
He was remanded into custody and will appear before Huntingdon Magistrates’ Court on Thursday.
It was part of a Greater Manchester Police (GMP) investigation into “multiple reports of threatening and abusive phone calls, emails and letters” targeting Ms Rayner, the MP for Ashton-under-Lyne.
A 52-year-old man, who has not been named, was arrested on Wednesday in Halifax over abusive phone calls received on 15 October – the day Sir David Amess was murdered.
The man was arrested on suspicion of malicious communications and has been released on bail as enquiries continue.
A third suspect, a 70-year-old man, was arrested on Thursday morning in South Yorkshire, on suspicion of malicious communications.
Police said the man had been arrested over abusive emails received on 16 October, and he remains in custody for questioning.
“Enquiries remain ongoing and GMP continues to work in partnership with Cambridgeshire Constabulary and South Yorkshire Police,” a spokesperson added.
Police did not name the victim but Ms Rayner’s office confirmed that she was the target.
A spokesperson said:“Angela and her staff have received a number of threatening, malicious and abusive communications in recent weeks. 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.
”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.”
The arrest came amid calls for action over threats and abuse towards MPs following the murder of Sir David.
The home secretary commissioned a security review that saw police contact all MPs to check sufficient arrangements were in place.
Anyone with information is asked to call police via 101, visit the Greater Manchester Police website or contact Crimestoppers anonymously on 0800 555 111.
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