Critics of plans to exempt MPs from Freedom of Information laws are preparing to try to "kill off" the bill again, when it is debated on Friday.
The Bill would exempt peers and MPs from FOI requests
Labour's parliamentary committee has asked its MPs to support the bill, proposed by Tory MP David McClean.
Lib Dem MP Norman Baker said the move was "very unusual" and proved it was a "government bill in all but name".
The bill's supporters say it would guarantee confidentiality for an MPs' correspondence with constituents.
But critics believe it could be used to cover up information, like expenses, saying private correspondence is already covered by data protection laws.
Opponents, who include MPs from all three main parties, thought they had effectively killed it off by "talking out" the bill - debating it for so long it ran out of Parliamentary time.
But in an unusual move, it is returning to the Commons on Friday.
Private Member's Bills rarely become law without government support as they need to be granted Parliamentary time to be debated - but on this bill the government has said it is neutral.
The Lib Dems, who are opposing the bill, have pushed Tony Blair to say where he stands - but the prime minister has said it would be "inappropriate" to comment.
Another critic, Labour MP David Winnick believes party managers have been "actively encouraging" Labour's parliamentary committee to back the Bill.
Backbench MPs have been sent an e-mail by the committee, urging them to turn up to support it on Friday.
But PLP committee member Martin Salter denied that party managers had a hand in the e-mail.
He said the committee was backing the bill because it would "plug the dangerous and unintended consequence" of private correspondence between an MP and a constituent being released.
PLP chairman Tony Lloyd has also said the bill addressed a legitimate concern, and would not restrict access to information on MPs' expenses.
But Mr Baker told the BBC News website it was "highly irregular", as they were asking Labour MPs to support a Conservative Bill, which was in opposition to Labour's official policy and its own FOI Act.
He said both the Labour and Conservative front benches had "actively supported it by their actions."
"If they think it's a good idea they should come out and say something about it," he said.
"If Gordon Brown [the favourite to succeed Mr Blair as prime minister] made it known he doesn't want to go ahead with this ... then Labour MPs will vanish on Friday. It's up to him to say something."
He said opponents would obviously be trying to stop the bill going through, but did not want to elaborate on plans for Friday.
Campaign group Unlock Democracy director Peter Facey also said: "This has now become a key test of Gordon Brown and his fellow Labour leadership contenders.
"On Friday Brown pledged to make government 'more open and accountable' ... over this next week we call on him to put words into action and to clearly indicate that he opposes David Maclean's Bill."