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The company said around 13 of its crown post offices failed to open because of industrial action by members of the Communication Workers Union in a row over transferring services from post
offices to WH Smith stores.
Hundreds of union members were on strike until midday in protest at plans to close 85 crown branches and move services to the High Street retailer.
The union regards the move as privatisation and has warned that 1,500 jobs will be axed and workers who remain will suffer pay and pension cuts worth thousands of pounds.
A Royal Mail spokesman said the vast majority of crown offices were open despite the strike, while sub post offices were not affected by the dispute.
The union's national officer, Andy Furey, said: "Members have been left with no alternative but to take strike action as management is steam-rolling ahead with closures of crown post offices
across the UK."
The union has warned there will be further industrial action unless the post office returns to negotiations with an improved offer on pay and job security.
Meanwhile, postal workers were clearing the backlog of mail caused by last Friday's 24-hour strike in a separate row over pay and jobs.
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