Letters from former minister Denis MacShane admitting expenses abuses cannot be used to prosecute him because they are protected by Commons rules.
Officials said parliamentary privilege meant the key correspondence was withheld from police when they launched a probe into the MP two years ago. And the documents are still not legally admissible - even though they were published in a Commons sleaze report.
The situation emerged after the Standards and Privileges Committee detailed how Mr MacShane knowingly submitted 19 false invoices over a four-year period. The cross-party group said the invoices were "plainly intended to deceive", branding it the "gravest case" they had dealt with.
The former Labour Europe minister pre-empted the recommended punishment of 12 months' suspension from the House by announcing his resignation as an MP. He insisted he had not gained personally from the abuses but wanted to take "responsibility for my mistakes".
"I have been overwhelmed by messages of support for my work as an MP on a range of issues but I accept that my parliamentary career is over," he said. "I appreciate the committee's ruling that I made no personal gain and I regret my foolishness in the manner I chose to be reimbursed for work including working as the Prime Minister's personal envoy in Europe."
A senior Labour source said: "Denis has done the right thing."
Parliamentary Standards Commissioner John Lyon found the MP had entered 19 "misleading" expenses claims for research and translation services from a body called the European Policy Institute (EPI), signed by its supposed general manager.
However, the institute did not exist "in this form" by the time in question and the general manager's signature was provided by Mr MacShane himself or someone else "under his authority".
"The effect was that, unbeknown to the (expenses) department, Mr MacShane was submitting invoices to himself and asking the parliamentary authorities to pay," the Commissioner said.
Scotland Yard dropped the case against Mr MacShane in July after receiving advice from the CPS on an initial evidence file. The force said on Friday: "We are aware of the report and will be assessing its content in due course."