LONDON (Reuters) - British opposition Labour lawmaker Angela Eagle, who this week dropped out of the race to oust party leader Jeremy Corbyn, has been advised by police not to hold her regular advice session with constituents due to safety risks, her office said on Thursday.

Last month, Labour lawmaker Jo Cox was murdered as she attended her "surgery," one-to-one meetings when members of the public have the opportunity to raise issues with their local lawmaker.

A 52-year-old local man, Thomas Mair, has been charged with Cox's murder and will go on trial in November.

"We have received advice from Merseyside Police that the safety of Angela, her staff and constituents cannot be guaranteed," said a staff member at Eagle's office, which was vandalized last week.

A spokesman for Eagle said Friday's canceled surgery had been due to be an open drop-in session. Future surgery sessions, due to resume in September after a scheduled August break, would now be appointment-based, he said.

Labour is locked in a bitter internal power struggle, with Corbyn refusing to stand down despite most of his policy team resigning and Labour lawmakers overwhelmingly backing a vote of no confidence in his leadership.

Eagle, formerly the party's top business spokeswoman, triggered a leadership contest earlier this month by challenging Corbyn. She withdrew from the race this week after receiving less support from lawmakers than rival Owen Smith.

The staff member said the office in Wallasey near Liverpool in northwest England was still open to members of the public and could also be contacted by phone or email.

On Tuesday, police said a 44-year-old man, who had been arrested on suspicion of making threats to kill after an email was sent to Eagle, had been released on bail pending further enquiries.

Eagle has previously said Corbyn, who has strong support among party grassroots members, "needs to get control of the people who are supporting him". Last week Corbyn said he condemned any violence or threats.

(Reporting by Kylie MacLellan; editing by Stephen Addison and Giles Elgood)