Royal Mail workers at a delivery depot in Whitehall, Bristol, have voted four to one in favour of strike action over what they say are ongoing job cuts.
The ballot follows a vote at the Montpelier depot in which staff came out seven to one in favour of striking.
Communication Workers Union area official David Wilshire said there could be "a long summer of disruption".
Royal Mail said the strike action would "only hurt our customers" and urged the CWU not to "call our people out".
A statement from Royal Mail said: "The threat to customers of damaging industrial action is completely at odds with the CWU's repeated claim to support modernisation.
"We urge them to act accordingly and not to call our people out on strike action which can only hurt our customers and damage our drive to build a strong and sustainable future for Royal Mail.
"Industrial action will not modernise Royal Mail, it will simply disrupt the service to which customers are entitled, lead to an even greater loss of business and leave Royal Mail far less able to protect full-time jobs."
Strike ballots are due to be held for a further 24 units in the Bristol area including the sorting centre at Filton.
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