Football Association chairman Greg Dyke has written to Fifa's top executives demanding a report into alleged World Cup corruption is published in full.
A 42-page summary report was released last week but quickly criticised by Michael Garcia, who spent two years investigating the claims of wrongdoing.
The report cleared Russia and Qatar of corruption over their 2018 and 2022 bids but said England broke rules.
Dyke wants Garcia's findings published, writing: "We cannot go on like this."
Garcia is due to meet the report's author, Fifa ethics judge, Hans-Joachim Eckert, on Thursday to discuss his criticisms.
He has said Eckert's report "contains numerous materially incomplete and erroneous representations".
Garcia also previously said the report should be published in full, although Eckert rejected this, in part to protect those mentioned in it.
But Dyke, who last week called Eckert's report "a joke", believes it is an essential first step towards English football regaining some degree of trust in Fifa.
"As you probably know the reputation of Fifa was already low in England and much of Europe before the events of last week," said Dyke in his letter.
The "failure" to publish Garcia's full findings, and Garcia's own criticisms, had "resulted in a further decline in public confidence of Fifa", Dyke continued.
"We cannot go on like this. Complete transparency is required if the actions of all those who bid, including England 2018, are to be judged fairly."
Earlier on Monday, former FA chairman David Bernstein urged the FA to lobby Uefa for a European boycott of the next World Cup, unless Fifa implements reform.
But Dyke was never likely to take such drastic action, instead writing to Fifa's senior executives: "Urgent action is needed if confidence in Fifa is to be rebuilt in England. The FA is of the view that this action should start with the full publication of Mr Garcia's report."
In his report, Eckert accused the FA of trying to "curry favour" with former Fifa vice-president Jack Warner, who quit in 2011 amid bribery allegations.