The Royal Mail national strike in 2007 was also about modernisation
Postal workers have walked out in the Midlands, Bristol, Yorkshire and south- east England.
The Communication Workers Union says it aims to stop deliveries in and out of London for 24 hours.
The bad feeling between the union and ministers has continued, with the CWU calling yesterday's comments by Lord Mandelson "a disgrace".
The business secretary had accused the union of trying to "frustrate" modernisation at Royal Mail.
Lord Mandelson said the union had to "wake up" to stop the Mail's "further decline."
The CWU is due to ballot next week on whether to hold a national strike for the first time since 2007.
CWU rep Sajid Shiakh: "The union has never been against modernisation"
The union's deputy general secretary, Dave Ward, accused ministers of encouraging Royal Mail to "destroy" the union:
He said: "Lord Mandelson's comments are an absolute disgrace.
"Postal workers note that this government - a Labour government - are abrogating their responsibilities", he told Breakfast on BBC Radio 5 live.
Mr Ward said the government wanted Royal Mail managers to modernise the service, no matter what the cost: "They're now saying to those people, we're giving you the green light; get in and destroy this union."
Exam Results
Royal Mail insisted that Thursday's delivery of A-level results would not be affected.
A spokesman said: "Well over 90% of our people and more than 90% of our operational units are working normally.
"We cannot understand why the union is claiming to support modernisation when it's pursuing a policy of actively opposing the changes we need to make to ensure there's a successful future for the business.
"We have held more than 50 meetings with the union in recent months and the door for talks with the union remains open."
In June, Lord Mandelson announced plans to sell off part of Royal Mail had been delayed because no suitable buyer had been found.
Some businesses have warned that, if the strikes continue, they will cause problems in the wider economy.
Gay Slade, who runs a feng shui business via eBay, said the dispute was "adding misery upon misery".
She said: "It's getting to the point now where we're getting really worried that this is going to carry on too long.
"Nothing seems to be being done to resolve the issue. It's just going on and on.
"They're now talking about balloting for an all-out strike in October, which will be coming up to the peak period for internet sellers.
"It could ruin people's businesses and ruin people's lives. People could lose their homes over this."
Earlier this year, Royal Mail warned it was in a "very tight financial position" and had to cut costs.
In 2008, all four parts of Royal Mail were profitable for the first time in almost two decades.
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