Members of the Communication Workers union voted by 63% in favour of industrial action in support of a 5% pay claim. Just 37% voted against holding a strike. The turnout among the 145,000 workers balloted was 65%.
The general secretary of the CWU, Billy Hayes, said: "I am pleased that the members have shown their feelings so clearly."
The union will decide next week whether or not to name strike dates, but Mr Hayes said there would be no action for at least a fortnight.
Mr Hayes said he hoped that the management of Consignia, formerly the Post Office, would meet union demands and therefore avert strike action.
"We will discuss arrangements to implement industrial action early next week, but I sincerely hope that the result will encourage management to look again at their position so that we can reach an agreement rather than take action," he said.
The company said that given ongoing losses, it would be hard-pressed to increase its pay offer to the unions.
Consignia has offered a 2% increase, with a further 0.5% on offer if customer quality of service targets are met.
"It's regrettable that the union even embarked on a ballot when it knows that the company is losing £1m a day. A strike would be catastrophic for us all. We simply cannot afford it," a company spokesman said.
"Under the circumstances the offer is wholly realistic and we have said that we are happy to improve it, if we can improve our efficiency at the same time."
The union hopes to see basic pay levels rise to a minimum of £300 a week by October 2003.
Postal workers last held national strikes in 1996, when workers protested over pay and conditions.
The CWU said it was willing to meet Consignia at any time, with or without the assistance of the conciliation service Acas.
