So, as an update, I did give her a discount (only because if she get's real pi$$y about things it will cost me more to deal with). Basically I took the time off I spent trying to locate the cable I damaged and the time taken to repair it. Nothing more. The discount is conditional on prompt payment. My terms for domestic customers are 14 days, so after that point, the full amount will be due.
I wrote her a letter that went with the quote laying out a few facts about my charging scheme, indicating how much she'd already saved because I made the choice to bill her by the day rather than the hour (I included a day by day time breakdown as part of that). I also made it clear that as an employee of my company, I'm entitled to mandatory breaks in accordance with the law and that whilst we may appear to be manual workers, we are in fact knowledge workers that require in-depth knowledge of both the general rules and the installation being worked on, and in the absence of good documentation about said installation, inspection and testing requires a methodical approach that sometimes requires us to stop, take a step back and think about what it is we're working on.
It also included some useful advice about avoiding this kind of situation arising again, specifically how to investigate the people she employs in terms of scam membership and also a rough outline of notifiable work.
It has been said, we shouldn't be head scratching in front of the customers. Whilst generally I agree, particularly when asked questions, as I've said above, there are times when it is necessary to just stop and think. But to put it into perspective, on this job, I reckon I actually spent less than an hour just thinking. However, from her perspective there were times when it may have appeared I wasn't doing much... because I was sat in front of the board, marking up cables, making notes, and testing. The rest of the time, I was running round her house testing, investigating, fixing and re-testing.
Anyhow, thanks for all the advice. I've learned my lesson and from now on, it's going to be EICR and remedial work as separate items, even if the timing is tight.