Finding that out is done under "dead" testing....
Every socket is taken off the wall, every leg tested for continuity to "map out" where each cable goes... ie between which sockets. From that, the location of the break can be generally worked out.
A martindale socket tester wont do it... it needs to be a professional multi function tester.... (although some things can be done with a lesser basic multimeter)
Fault finding is a costly process. It could take 5 minutes to find the problem, it could take 5 hours.
If you are not happy with what the electrician has charged you with, then there is no reason not to try someone else for the remedials