may not be as big as a complete rewiring of the house, so happens among other talents I am qualified as a 17th edition electrician, never worked as a true sparkie before however or rewired a house, was gifted the qualification from an old employer who put me though the electrical crash course to get the paperwork for one specific reason, so I could wire up racking server cases within the Data Centre where was working, so don't claim to be a real expert on the subject of rewiring the entire house, but probably know more about it than the average computer tech or joe in the street.
But my best guess would be the fault is related to the Consumer Unit or the wiring within the consumer unit, since realy if turning on a light is causing issues with the sockets in the house the 2 circuits should not be linked between the lights and the sockets, unless they are poorly wired in a the Consumer Unit or the Unit its self is faulty and causing issues by allowing separate circuits to interfere with each other, so could just be a new Consumer Unit fitted to fix everything, these things are always been updated with new regs, am not a sparkie so don't follow the latest regs, but know that if you have a really old out dated consumer unit that would not even meet modern regs, then getting a new up to date Unit with double RCD's and that will meet the latest regs is not a bad idea all around, and you can pick up a really good one for under £100. Then you would be talking just a couple of hours work for a good sparkie to come fit it and test the socket circuits while they are there.
So I would would say £100 for the Unit, assuming your unit is out dated, then £50 per hour for a Sparkie to fit it and test the sockets circuits while they are at it, a sparkie working his guts out could realistically fit it in under an hour, but to make it worth there while there going to take a couple of hours to fit it taking it easy, then want paying for an extra hours break while they are there, so your more likely to get charged around £150 for fitting, maybe even £200 (or 4 hours at there given rate) if your guy wants to take the piss, any more than that I would send them home packing, and any sparkie saying they don't know how long its going to take them to fit the unit when looking for a quote is a straight up liar, its there job, there own business ffs, they know exactly how long its going to take them so if they say they don't know on the phone skip them and find another more competent Sparkie who does know, and is not giving you a stupid time figure to take the piss.
But calling for a complete rewire of the house over this you would have to be joking, that would cost 1000's and leave you with a second bill after they're finished when you need a plaster to come clean up there mess, then you will find after they are finished your still left with the need to redecorate to finish the job of yourself getting your house back to how it was before they started, unless you want to hire a decorator and ship out even more money.
But that's all pointless because you already know that if an action like flushing your Toilet or turning on a light is effecting your wall sockets, then you can isolate on that single circuit been effected (the sockets), could be the wiring is just fine and the Consumer unit alone fixes everything, else if there is an issue within the circuit its self, then the Sparkie will be able to go round the circuit visiting each wall socket on the way till they find the drop in the Ohms level where a single wire from one socket to the next is the problem, another couple hours at the most, another hours work even to change a Wire from one socket to the next if that's even necessary, but I doubt it would even take that, problem is more likely to be at one of the sockets with bad wiring so changing a single wall socket in your house could fix everything if its just a bad connection into the socket, again another hours work, wall sockets cost pence, so this would be best case scenario really if its just bad wiring at a single socket, you would need the entire circuit tested though because if your loosing current to one of your sockets then odds are that the fault is wireing at an earlier socket on the in the circuit, or still the Consumer Unit its self been the number 1 suspect still as in the first place.
Honestly I would not worry about having to move house just get because you think you need a complete rewire because that is just bollocks, when you have fault within a single circuit, just get that one circuit tested along with the Consumer Unit, no more is necessary.