In his letter to Sir Laurie, Farage said: "The chancellor conducted a sustained public and media campaign portraying the public finances as being in a state of collapse in order to prepare political ground for approximately £30bn of tax increases which, on the OBR's own numbers, were discretionary policy choices rather than unavoidable fiscal necessity.
"The British people are now facing the heaviest tax burden in generations on the basis of what increasingly looks like a sustained misrepresentation of the true fiscal position."
In his reply to Farage explaining his decision not to launch an investigation, Sir Laurie said: "It is not within my remit to consider the collective actions of government departments or individuals other than ministers."
He added that he was also not able to look into "questions of market regulation" which are the responsibility of the Financial Conduct Authority FCA).
Conservative shadow chancellor Sir Mel Stride had already asked the FCA to investigate "possible market abuse" over pre-Budget leaks.
Measures including a freezing of income tax thresholds, a pay-per-mile levy on electric vehicles and a tourist tax were all leaked ahead of the Budget.
"Confidential market sensitive information appears to have been spun, leaked and misused - and markets, businesses and families have paid the price," Sir Mel said.
The FCA has said it has not begun an inquiry and that the way the government communicates is "a matter for Parliament through its accountability mechanisms".
It has requested the details of a leak inquiry launched by the Treasury earlier this week.
Speaking to a committee on Tuesday, a senior official at the Office for Budget Responsibility said he did not believe the chancellor had been misleading when she said, ahead of the Budget, that the state of the public finances was "very challenging".
Prof David Miles said that despite the better-than-expected tax receipts the chancellor still faced "very difficult choices".
He also said the OBR had not found Budget leaks to the media "helpful".