You should budget for replacing it at some point.
In particular, if you’re doing DIY electrics elsewhere then a replacement with RCDs will make things safer if you get something wrong while e.g. wiring a new light.
I hope you have the cover for the fuses. I note also two screws are missing from the panel.
It is understandable to want to turn off single circuits. For example, you might want to have the lights on so you can see what you’re doing while working on a socket. You shouldn’t do this, but I bet a lot of people here do it anyway (I know I do - but I have RCDs). The safest way to do this is to switch off the main switch, remove the fuse cover, remove the fuse, replace the cover, turn on. Repeat in reverse when done. Double-check for live wires before touching anything, in case it’s not on the circuit you thought it was. Of course that doesn’t help with your computer powering off.
OK, new RCD units seem to be about £150 -£200 I guess installation would cost as much again? Perhaps it's worth doing now.
It's not just the computer. Also clocks on the oven and central heating. Just too bad.
I do note that my fuse box has two missing screws. I do have the cover - I just removed it for the photo. It doesn't have any wording on it about turning the power off before removing fuses.