Rayner’s head of communications Jack McKenna has been placed under investigation on suspicion of a personal data breach relating to another Labour staff member.
It is understood that he denies any wrongdoing and is consulting his union.
Mr McKenna manages the deputy leader’s relations with the media as well as writing her speeches, and has previously been forced to deny rumours that he briefed reporters about differences between Starmer and Rayner.
He is understood to have learnt of his suspension from a reporter with the Sunday Times, raising questions about the party’s handling of his own personal data.
Starmer has repeatedly denied any rift with his deputy, who cannot be sacked from her position because she was directly elected by party members.
In an interview published just hours before Mr McKenna’s suspension, Sir Keir said: There is no personal issue between me and Angela. We’re friends, we get on, we talk a lot.
“We bring different things to the table . . . the two of us together make each other stronger. She’s politically astute and invaluable to me as a deputy leader and to the party.”
The leader risked a clash with his deputy earlier this week by launching a reshuffle of his shadow cabinet without involving her. Ms Rayner was informed of the shake-up as she prepared to deliver a long-planned speech about sleaze.
It followed a botched reshuffle in May in which the deputy leader resisted Starmer’s attempt to strip her of some of her responsibilities.
The Sunday Times reported that McKenna’s suspension was understood to be linked to a now-deleted tweet by a journalist referring to a row between shadow Scotland secretary Ian Murray and Labour’s head of policy, Claire Ainsley about whether one of his aides would be sacked. Labour headquarters is investigating a claim that McKenna breached “personal data” by briefing the press about the row.
A Labour spokesperson declined to comment on the affair, telling The Independent: “We never discuss staffing matters.”
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