Sorry for the late reply but I wanted everyone to know I had read their replies. Thanks.
I managed to fix the switch, the plastic innards of the dead man's handle had fallen out of alignment, so I am back mowing for now.
I will look to replace it in the near future. I was thinking of a Honda petrol mower but I notice that the cheaper models have a steel deck that reviewers say rusts. I have been encouraged by the posts here about Lithium powered mowers, so I will look into those when the time comes.
At previous houses, I have not had the problem with the cable. I think the problem is the position of the socket. In the diagram above, the socket is in a corner. That's the best position for it but here my socket is in the middle (of the edge). I guess the only way would be for me to cut from the middle of the lawn out.
Thanks again, Stephen.