The Football Association and the Scottish Football Association have called for Fifa to postpone its presidential election.
Current president Sepp Blatter is the only candidate for the 1 June election after Mohamed Bin Hammam's withdrawal.
The FA now wants the vote delayed and an independent body to recommend "improved governance" of Fifa.
An SFA statement added: "The election should be rescheduled to facilitate a period of consultation."
The United Kingdom Home Nations are due to have discussions on Tuesday to discuss a joint stance.
''Discussions are going to happen in the next 24 hours and that [calling for the election to be postponed] will be a topic of conversation,'' Jonathan Ford, the FA of Wales chief executive, told BBC Wales.
The English FA recently chose to abstain from voting following allegations of corruption against world football's governing body.
And FA president Prince William has backed the calls for the election to be delayed.
A St James's Palace spokesperson told BBC Sport: "The Duke of Cambridge, as President, has been kept informed of the FA's proposals and is fully supportive of the Chairman and the initiatives the FA has recommended.
"He considers the transparency of the international governing body to be integral to the good governance of the game."
FA chairman David Bernstein said in a statement: "On 19 May, 2011 the Football Association announced it would be abstaining in the forthcoming election for the Fifa presidency.
"There were two main reasons for this decision. First, a concern, that a series of allegations relating to Fifa ExCo Members made it difficult to support either candidate.
"Secondly, a concern about the lack of transparency and accountability within the organisation, contributing to the current unsatisfactory situation.
"Events of the last few days have reinforced our views, and we call on Fifa and ask other national associations to support us with two initiatives.
"First, to postpone the election and give credibility to this process, so any alternative reforming candidate could have the opportunity to stand for president.
"Secondly, to appoint a genuinely independent external party to make recommendations regarding improved governance and compliance procedures and structures throughout the Fifa decision-making processes for consideration by the full membership.
"This has been a very damaging time for the reputation of Fifa and therefore the whole of football.
"To improve confidence in the way the game is governed at the very top, we believe these requests would be a positive step forward and the minimum that should take place."
The SFA later added to the growing concern over the running of football's world governing body.
"The events of the last two days, in particular, have made any election unworkable," added its statement. "The integrity and reputation of the game across the world is paramount and the Scottish FA urges Fifa to reconsider its intentions, and calls on other member associations to consider the long-term implications for the game's image.
"We also propose the following actions: Fifa should appoint a wholly independent ethics committee; a significant comprehensive plan should be formulated and presented by Fifa to its members regarding essential changes to its governance, decision-making processes and transparency; a new date is set for the presidential election, giving suitable candidates time to prepare and present their plans for a more transparent and accountable Fifa."
Whether the two FAs will receive the support of their counterparts remains to be seen but Blatter, speaking defiantly at a news conference on Monday, seemed set on making sure the presidential election went ahead unless three quarters of Fifa's congress of 208 voted otherwise.
Blatter, 75, is vying to be re-elected for a fourth term and, despite insisting Fifa was not in crisis, the FA's latest move comes amid world football's governing body being undermined by a series of corruption allegations.
Following question marks being raised over the legitimacy of the 2018 and 2022 World Cup bidding processes, the Fifa presidential election race has been tarnished by further claims of wrongdoings.
Bin Hammam, president of the Asian Football Federation, and Fifa vice-president Jack Warner have been provisionally suspended by Fifa's ethics committee over allegations that financial incentives were offered to Caribbean Football Union members.
Blatter was also investigated following a charge against him by Bin Hammam, although Fifa's ethics committee did not find the president had a case to answer.
Bin Hammam has appealed against his ban, while Warner revealed an e-mail in which Fifa general secretary Jerome Valcke suggested Bin Hammam "bought" the 2022 World Cup, which will be held in Qatar.
Valcke responded by saying his remarks were taken out of context before the latest twist to the turmoil surrounding Fifa resulted in major sponsors Coca-Cola, Adidas, Emirates and Visa expressing their concern at the damage being done to Fifa by the alleged claims of corruption.
Meanwhile, anti-corruption watchdog Transparency International backed calls for an independent body to delve into the goings on within Fifa.
"Free and fair elections cannot take place when there is a suspicion that voters may have been swayed," Sylvia Schenk, senior advisor on sport to TI, said in a statement.
"Fifa delegates know that they must clean house if their vote is to have legitimacy."