I had the same problem, I knew the house had rubber cables, wired 1954, and it needed a rewire, dad said "I am not living in a building site, you can rewire it when I'm gone." which is what happened, the cables were crumbling by time I got it rewired.
But a new consumer unit is done in a day in most cases, it is not a full rewire, likely an EICR is the way to go, as if it says something wrong, you have some thing to try and persuade him with. I did get a new consumer unit fitted, which was like you already have, as the electrician fitting it could not get the RCD to hold in, he was not really a good electrician as he used the GPO party line earth rod and cables as his main earth so 1 mm bare earth cable on a TT supply, I got house on a TN-C-S supply.