I used to worked in the Woking area (as a sparky) and have assessed electricians in the Woking area and they all say the same.
Not putting a too finer point in it but Woking BC are in the "hands of" the NICEIC, if you get my drift. Woking BC are anti-anything that is not paying funds to the NICEIC and for good reason (as far as they are concerned - cough-cough).
Refer it and watch them change their mind - any suggestion of a possible investigation focuses the attention somewhat!
Any LABC can legally sub out the part P testing. The contractors are working on their behalf. This is the only time 2nd party testing is allowed for the part P rules.
Regarding the fees, most LABC are the same and try the old 'we are doing it for the good of the community' bit.