Communication Workers Union spokesperson Andy Furey said Post Office workers did not want to strike, but were determined to "secure a fair settlement." He said he was optimistic about agreement being reached.
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Extracts released by 10 Downing Street suggest Mrs May will say the UK will not settle for a "half-in, half-out" policy.
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In her Brexit speech on Tuesday, the Prime Minister is set to urge the EU to forge a fair trade deal or risk commercial war.