Prescott launched his attack after Agriculture Minister Nick Brown was forced to admit he is gay when a former lover tried to sell his story to a Sunday newspaper.
Brown is the third member of the 22-strong cabinet linked to gay rumors or disclosures in two weeks.
"I think it's quite deplorable. They [newspapers] seem to be judge, jury, and executioner in this matter. It's totally unacceptable, and I think British public opinion's against it also," Prescott told the BBC.
He called on the Press Complaints Commission, a voluntary industry watchdog, to clamp down on intrusion.
Most papers on Monday expressed sympathy for Brown, but the Sun said the revelation that a fourth member of Prime Minister Tony Blair's cabinet was gay had set alarm bells ringing.
"Tell us the Truth, Tony" the paper, owned by media mogul Rupert Murdoch, said in a front-page editorial. It said it did not want to pillory homosexuals but asked: "Is Britain being run by a gay Mafia of politicians, lawyers, Palace courtiers and TV bigwigs?"
Brown went public about his sexuality after The News of The World, the Sun's stablemate and Britain's best-selling Sunday paper, was approached by a former lover with what it said were "a series of fanciful and lurid allegations."
The minister, 48, acknowledged that he occasionally gave his partner small sums of money but denied he ever paid for sex.
Cabinet colleagues quickly closed ranks behind Brown, a behind-the-scenes fixer who joined the cabinet in July after serving as chief whip, or parliamentary business manager.
Blair also rallied behind Brown, saying he would keep his job.
"Nick Brown has given a full account of this relationship to the prime minister, and the prime minister is satisfied with that account," Blair's Downing Street office said in a statement.
But Brown made his bitterness clear in a brief television interview on Sunday. "I had rather hoped I could have a private life like other people," he said.
It was the second embarrassment in short order for Blair's government, which is coming under fiercer media scrutiny now that the novelty of its first 18 months in office has worn off.
Welsh Secretary Ron Davies resigned last month after becoming the victim of an armed robbery when he befriended a stranger one night in a London park known as a homosexual meeting place.
Davies denied newspaper allegations that he was involved in a gay sex encounter, but he gave no clear explanation of what had happened. During speculation about Davies' sexual orientation, a newspaper columnist said Trade Secretary Peter Mandelson is gay. Mandelson did not respond to he comment.
The previous Conservative administration of John Major was dogged by media probes into the financial and sexual peccadilloes of ministers, and Prescott was careful not to claim a special dispensation for Labor or to back a new privacy law.
"I've said myself that I'm not in favor of that [legislation]. But there is a balance in this, and at the moment some of the editors have decided that the balance should be more to what is to do with selling papers," he said.
As in the United States, where voters proved to be indifferent to President Bill Clinton's affair with White House intern Monica Lewinsky, the British public seem to care little about the private lives of the politicians they elect.
The steady relationship enjoyed by another gay cabinet minister, Culture Secretary Chris Smith, was written up in glowing terms recently by the Daily Mail, which is avidly read by politicians keen to tap the pulse of Middle England.
"Over the past decade or so, a new sense of tolerance has started to pervade much of the British electorate," The Times said in an editorial on Monday. "If [Brown's] admission is indeed met with indifference, it will reflect a welcome change in public attitudes towards politicians' private lives."
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