The titles to go include the Derby Trader, Ilkeston Trader, Ripley Trader, Belper Bugle, Peterborough Herald and Post, Stamford Herald and Post, Whittlesey Standard, and Deepings Standard.
Up to 23 people could be made redundant, including six editorial employees and 14 advertising staff. Consultation has reportedly begun with those affected.
Trinity said the decision to withdraw from these markets would allow its Midlands division to refocus attention on its remaining portfolio of weekly newspapers, adding that it had no plans to close any other publications.
Steve Brown, regional managing director of Trinity Mirror Midlands, said: "It is a very sad day when newspaper titles close and we looked hard at alternative measures to try and prevent this decision.
"However, the remaining titles in the Trinity Mirror Midlands marketplace remain strong and the management team is focused on continuing to grow audiences and products across the rest of the region."
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