Invoices obtained by Conservative group leader and councillor Peter Golds and journalist Ted Jeory show that the council spent £41,000 on PR and public affairs agency Champollion and £82,000 on lawyers Taylor Wessing, as well as £5,400 on a QC.
Cllr Golds claimed the money paid to Champollion was to coach the mayor for his interview with the BBC for a Panorama programme called 'The Mayor And Our Money', which was aired in March ahead of the local elections.
However, a more detailed schedule of fees proposed by Champollion, obtained by Jeory, show the cost of preparing the mayor for the Panorama interview was £4,200 and the overall sum also covered strategic advice and crisis comms.
The council has not contested the figures or the claim that Champollion was paid to coach the mayor, while Champollion declined to comment.
In a letter to council officers, Cllr Gold said Tower Hamlets had employed lawyers "trying to prevent a BBC programme that is impartial" and claimed he had been blocked "at every turn" from obtaining information about the amounts spent.
The council spent no money preparing for another interview with Rahman, shown on Islam TV around the same time as the BBC broadcast, because this programme was "promoting the mayor", Cllr Golds claimed.
He said: "The council’s hypocrisy is breathtaking. Taxpayers’ money was used to try to prevent the mayor being subject to any criticism, and the council is now trying to prevent the public finding out details of how their money was spent."
The council said it received a dossier from a "whistleblower" working on the Panorama programme ahead of broadcast, who said it would be "unfair and misleading".
The council said it had to take action to "communicate our concerns" to the BBC to ensure balanced coverage because it would air before the mayoral election.
A council spokesman added: "There was no in-house legal experience or capacity to deal with issues of journalistic standards and editorial compliance, so suitably experienced external legal firms were approached to pitch for the work.
"Taylor Wessing was selected and advised on the operation of BBC guidelines, based on its experience of tackling investigative reporting and regulatory compliance by the BBC and also on the editorial decision-making processes within the BBC. It also advised on data protection considerations for the council that applied to the personal data revealed in the dossier."