The CAA's Flight Examiner Handbook clearly states that the FI who conducted the training flight must sign the logbook of the applicant and include his licence number if the flight was satisfactory.
An hour of aerobatics and tailwheel flying? Nothing wrong with that. But if the FI has to take control to stop you endangering the aeroplane or yourself, and if the instructor has to correct your poor RT or stop you infringing controlled airspace?
To be honest, there is no real issue. The only time I wouldn't sign would be if you were so utterly awful or overconfident that I had concerns about your ability to fly passnegers without risk to them. Is that very likely? Frankly, I doubt it. I've never heard of anyone ever having a 'training flight' NOT signed off.
And you most certainly would pay - unless, of course, the flight was in a Permit aeroplane whose Permit did not include use for flight instruction. The flight would then be entirely private. I've only done that once - but the applicant did pay for my fuel to drive to his aerodrome.