Charles Clarke says he has "serious questions about Jack Dromey's capacity" as Labour treasurer after the row over the £14m of secret loans to the party.
He says the fact Mr Dromey did not know about the loans meant "you have to wonder how well he was doing his work".
But Labour National Executive Committee chair Sir Jeremy Beecham says Mr Dromey is "innocent of any negligence".
Scotland Yard says it is dealing with three complaints against the party into alleged breaches of the honours system.
New rules
The investigation will focus on whether the Honours (Prevention of Abuses) Act 1925 was abided by, and to see if honours were given by Labour in return for loans or donations.
The inquiry will come under the auspices of the Specialist Crime Directorate and will be led by Deputy Assistant Commissioner John Yates.
"Jack Dromey has always carried out his responsibilities with great diligence and retained the absolute confidence of the NEC in ensuring that this issue is dealt with"
A Scotland Yard spokeswoman confirmed that three complaints had been received against the party, including one from Scottish National MP Angus McNeil. Another was made by Elfyn Llwyd, parliamentary leader of Plaid Cymru.
The probe comes after Mr Dromey sparked uproar last week when he said that he, and all the other elected party officials, had been kept in the dark about the loans arranged by Tony Blair's chief fundraiser Lord Levy.
After meeting on Tuesday the NEC said the party would bring in new rules and disclose publicly all new loans.
This comes amid claims, denied by the prime minister, that those lending money were being rewarded with peerages.
The NEC would also take back its "rightful responsibility" for all the party's funding to make it more "transparent".
Shortly after this announcement, Mr Clarke said of Mr Dromey: "I don't know why Jack behaved as he did."
He said any competent treasurer looked at the finances of organisations.
NAMES OF LABOUR PARTY LENDERS:
He rejected as "nonsense" a suggestion that Mr Dromey had spoken publicly about the loans to speed up the transition of power from Mr Blair to Chancellor Gordon Brown.
The NEC acted after it had been presented with a report commissioned by Mr Dromey.
Sir Jeremy said Labour would co-operate with the police inquiry, but accused the Scottish and Welsh nationalists, who made the complaints, of "opportunism".
In a statement, he said it was "absolutely clear that the reasons that NEC officers, including the elected party treasurer, did not know about the loans had nothing to do with any failings on their part."
He added: "Jack Dromey has always carried out his responsibilities with great diligence and retained the absolute confidence of the NEC in ensuring that this issue is dealt with."
He later told BBC Two's Newsnight Mr Clarke had not read the situation correctly and had spoken out of turn.
He said: "I think Jack has acted perfectly properly as treasurer. He shouldn't be criticised. I wouldn't have said it in Charles Clarke's position."
Downing Street has confirmed Tony Blair will be meeting David Cameron for discussions on party funding following a written request from the Tory leader.
Mr Blair's official spokesman said no date had been set but that talks were expected within the next few days.
Ministers are hoping to use the Electoral Administration Bill, which is currently in the House of Lords, to ensure all future loans have to be declared.
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