Board members from the Independent Parliamentary Standards Authority (Ipsa) have refused to reapply for their posts after Bercow insisted they could not have their terms automatically renewed, as had been expected.
Sources close to Ipsa believe Bercow's stance is part of a backlash from parliamentarians who are trying to destabilise an authority which has clamped down on expenses in the wake of the 2009 scandal.
The Speaker's office says this is not true and it is simply following legal advice.
In a tense exchange of letters over the summer, Ipsa chairman Sir Ian Kennedy dismissed the idea that Bercow was legally obliged to hold a full selection process – estimated to cost £100,000.
He also raised concerns over a "perception" that Bercow was seeking to neuter Ipsa by removing Sir Scott Baker, Jackie Ballard, Ken Olisa and Isobel Sharp "wholesale" in January.
In particular, Kennedy said that Bercow had suggested introducing a former MP to the selection panel for board members which might be seen as interference in the independence of the watchdog.
Kennedy wrote: "It is in nobody's interest for expenses once again to become a live issue in the shape of a debate about the future composition of the board and what this might say about Ipsa's role as an independent regulator.
"I make no apologies for pointing out the fact that there is much at stake here, not least the reputation and future standing of Ipsa and indeed the reputation of parliament itself."
In a letter in April, Bercow said the Parliamentary Standards Act 2009 "requires each board position to be subject to fair and open competition at the end of every fixed term.
"I have been advised further that were I, as Speaker, to direct that any appointment be carried out by any procedure other than on merit on the basis of full and open competition, that direction would be amenable to judicial review," he wrote.
Kennedy replied that an open competition might be seen as offering "placemen/women of parliament".
He said that the Speaker's suggestion that the selection panel could include the ex-Tory MP Peter Atkinson would "inevitably introduce a perception of party politics".
"This would be wholly undesirable given the need for Ipsa to be and be seen to be independent of political influence," he wrote.
Kennedy – whose own term does not end until 2015 – said the £100,000 cost of the selection process was not "a good use of public funds" and cautioned that the key review of MPs' pay and pensions could be hampered.
The process for appointing new independent board members was launched in August, and with successful candidates due to be announced over the coming weeks.
Ipsa confirmed in a statement on Tuesday that the independent board members had not reapplied for their posts.
Ipsa took charge of MPs' expenses in 2010 in the wake of the scandal that engulfed Westminster the previous year.
However, the strengthened rules angered many politicians.
The Speaker's office played down the row, insisting it was merely a disagreement over "legal interpretation" of the Parliamentary Standards Act.
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