Police have warned senior Labour figures to stop putting "undue pressure" on officers investigating "cash-for-honours" claims.
Blair aide Ruth Turner was arrested and released on Friday
Several senior Labour MPs have called the arrest on Friday of Number 10 aide Ruth Turner, who denies any wrongdoing, unnecessary and "theatrical".
But the Metropolitan Police Federation said this was not an "appropriate moment" to make such comments.
The Liberal Democrats said police were acting professionally and normally.
Ms Turner was questioned on suspicion of perverting the course of justice and was later released.
Culture Secretary Tessa Jowell said she was "slightly bewildered" as to why the arrest had happened early in the morning, with four policemen knocking on the door of Ms Turner - who was then released without charge.
"She has fully co-operated and she is a person of utter decency and conscientiousness and I am surprised," Ms Jowell said.
Former Downing Street aide Lance Price said: "It does look a bit theatrical.
"Ruth Turner has co-operated with the inquiry all the way through up until this point. There's been no suggestion that she wasn't willing to give police any help that they asked for.
"So it does seem pretty extraordinary to do the sort of dawn raid that we associate generally with people who are about to abscond justice and fly on a plane to Bermuda or something."
Former Home Secretary David Blunkett said he wanted "thoroughness, not theatre".
Mr Blair gave Ms Turner, who as director of government relations is one of his closest aides, his full backing.
'No-one above the law'
However, Metropolitan Police Federation chairman Glen Smyth told BBC News 24: "You get government ministers and senior members of the Labour party criticising the inquiry, which has frankly not even given a report to the Crown Prosecution Service yet.
"What sort of undue pressure are they trying to bring? If that's not what they are intending, it's certainly the impression that they are leaving for the officers involved and, I suspect, many other people.
"They should wait for the appropriate moment."
Len Duvall, the Labour politician who chairs the Metropolitan Police Authority, called on others not to try to "manipulate or pressurise" officers.
In a statement, he told critics that "no one in this country is above the law".
Liberal Democrat spokesman Lord Thomas of Gresford said: "Once the police had formed a reasonable suspicion of her perverting the course of justice, as they must have, it was their duty to act swiftly and professionally to preserve any evidence.
"That is commonplace, as any criminal lawyer knows.
"Pressure put upon the police by people in high places suggests that they want the investigation stopped."
Ms Turner was first questioned by police in September.
The Metropolitan Police inquiry into claims people gave political donations in exchange for peerages began after it emerged that a number of large secret loans had been made to the Labour Party before the 2005 general election, and that some of those lenders had subsequently been nominated for peerages.
The investigation later widened to cover the other main parties.
Police have so far spoken to about 90 people including Mr Blair and former Tory leader Michael Howard.
All deny wrongdoing. No one has been charged.