He added: "The concept, in my view, of all firms simply paying a percentage of turnover would create a very different landscape that would do away with professional indemnity cover, and FSCS and Fos levies, if only somebody at the FCA would be brave and do the suggested maths."
In its FSCS Funding Review, CP 17/36, the FCA reported on feedback that suggested without any PI cover, FSCS levies would have been considerably higher than they are currently.
The Funding Review stated: "Our modelling of the data from PIFs indicates that, over the past 10 years, of consumer claims made against PIFs, 84 per cent by value are met by a combination of PII and the excess."
When asked about Mr Bradley's communications, a spokesman for the FCA said: "We have engaged extensively with Mr Bradley, including explaining why it is not possible to carry out the calculation he has requested as we do not collect turnover data from all firms for fees purposes."
Independent consultant Rory Percival said: "There are pros and cons of any structure. A flat percentage, for example, would cost higher producing firms more.
"But it seems the basis of the charge is irrelevant to [Mr Bradley's] argument. Surely the argument is about the quantum and what it covers - ie everything - rather than how the cake is cut.
"The other thing is what is, and is not, in the FCA's powers to change. It can change how the cake is cut but doesn't have the power to make other changes, such as having a product levy instead."
The Personal Finance Society had been lobbying the government to change the funding structure of the FCA also, in creating a product levy rather than a firm-based levy, but this was ruled out by the FCA in the 2016 review.
However, Keith Richards, chief executive of the PFS, has called for a rethink of the FSCS levy.
As reported by FTAdviser last year, the PFS has called for a savings and investment monetary protection and education (SIMPEL) levy, collected centrally by government.