Wellingborough Prison will close by the end of this year with the loss of almost 600 prison places.
The Justice Secretary Kenneth Clarke said closing the category C jail in Northamptonshire will save £10million per year.
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Armed police have carried out a raid apparently linked to Wednesday's deadly terror attack in Westminster.
Six addresses have been searched as part of police investigations so far and seven arrests have been made.
A large part of Hagley Road in the south west of the city was cordoned off and later reopened.