Jack Straw, Labour's home affairs spokesman, admitted the shift as the Commons gave a Second Reading to a Bill extending MI5's role beyond counter espionage and anti-terrorism to a part in the fight against organised crime.
Two years ago, when the Government bent to pressure for scrutiny of MI5 and its overseas counterpart MI6 and set up the Intelligence and Security Committee, Labour tried to amend the legislation so that the committee would be answerable to Parliament.
Chris Mullin, Labour MP for Sunderland South, asked if this was still the position of the front bench. Did the leadership want to strengthen accountability or would the committee, comprising senior figures from both sides of the House, still report to the Prime Minister?
Mr Straw said that "of course" Labour wanted "to see intelligence agencies which are properly accountable to this House. The question is how best that can be achieved whilst maintaining the operational integrity of these agencies.
"These arrangements have been put in place under the 1994 Act. It is important that they are kept under review, and that if they need to be strengthened then measures are brought forward ... to ensure that they are indeed strengthened."
Spotting the shift behind the smokescreen, Tory MPs shouted to Mr Mullin: "The answer is 'No'." But a smiling Mr Straw came clean and told the House: "The answer is 'Maybe'.''
Mr Mullin also tackled Michael Howard, the Home Secretary, on the justification for the Security Service Bill. Mr Howard said it would enable MI5 to support the police in taking on criminal gangs, drug traffickers and racketeers.
He said the service had been responding to changing threats ever since it was founded in 1909, from German spies in its early years, communists through the Cold War and latterly the terrorist menace.
But Mr Mullin said it was "running out of threats" and that a new one was having to be invented to save the "rather bloated organisation" from spending cuts.
Pressure for the Bill to be amended to enshrine the primacy of the police in operations came from both sides of the House, including former defence secretary Tom King, chairman of the committee.
However there was no vote against the Bill, even from arch-critic Ken Livingstone, Labour MP for Brent East, who declared that the one time Tory MP Captain Henry Kerby was an MI5 agent and had been used while Sir Edward Heath was leader of the Opposition to spread rumours that he was a homosexual-and had had an affair with a Swedish diplomat. "MI5 should be broken up and any worthwhile bits given to the police," Mr Livingstone said.
Junior agriculture minister Angela Browning earlier defended the Government's response to "mad cow disease". Its stance was "ultra precautionary" she said in a debate launched by Labour's David Hinchliffe on fears of a link between BSE and the human disease Creutzfeldt-Jacob Disease.
Last month, farmers Stephen and John Thompson of Yorkshire were convicted of trades description offences including falsely declaring the age of a calf and not declaring it was born to a BSE-infected cow, he said.
Mrs Browning replied that of the 915 BSE cases reported by the Thompsons since 1988, 76 per cent had been traced to their original owners.Reuse content