Don Foster MP, the Liberal Democrat's culture and media spokesman, told BBC News that Lord Mandelson's move was "reckless and dangerous".
"There are many families whose children, unbeknown to them, might be illegally downloading but now their own access could be put in jeopardy by Lord Mandelson's proposals."
Mr Foster acknowledged that online piracy was "a major problem in the UK" but said overriding the opinions of Lord Carter and two secretaries of state was "bizarre".
The Conservative MP John Whittingdale, who is also chairman of the Culture, Media and Sport Select Committee, said he was broadly supportive of Lord Mandelson's proposals, but said that he may have inadvertently "killed his own bill".
"Personally I am on his [Lord Mandelson's] side; peer-to-peer sharing is the greatest threat to our creative industries," he said.
"I don't think people should have their broadband cut off, but there are measures to restrict speed which is better than prosecuting people so they get a criminal record.
"That said, I have severe doubts that the government can get this bill through in the time available as if there is any opposition to it - and there will be now - there will be a general election before it goes through."
Originally the Digital Britain report, published in June, gave Ofcom until 2012 to consider whether technical measures to catch pirates were necessary.
However, according to a statement from the Department for Business, Innovation and Skills (BIS) released on Tuesday, that timeframe is now considered "too long to wait".
Stephen Timms, minister for Digital Britain, said: "We've been listening carefully to responses to the consultation this far, and it's become clear there are widespread concerns that the plans as they stand could delay action, impacting unfairly upon rights holders."
It proposes that internet service providers (ISPs) are obliged to take action against repeat infringers and suggests that the cost of tracking down persistent pirates be shared 50:50 between ISPs and rights holders.
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