I am surprised at the number of very old Consumer Units (aka Fuse Boxes) I come across in homes, the type with that has rewirable fuses. Sure these old fuses boxes probably still do OK what they were supposed to do 30 years ago, but since then the introduction of more convenient and technically superior electrical safety protection devices for Consumer Units has been available. Also these new Consumer Units are not expensive compared to the value of a home or home improvement projects.
One example of a safety improvement with the new Consumer Units is dealing with the situation where a home owner hangs a picture using a screw or nail and accidently hits a cable buried under the wall plaster. With a new Consumer Unit very little electricity flows (not enough to give an electric shock to a human) before a switch automatically trips out to disconnect the electricity. With a rewireable fuse there will be a lot of electrical energy that flows for a little longer and a noticeable pop from the fuse when it blows, worse still it could be the screw or nail will remain live and the fuse will not blow at all!
I also tend to find that if a home has one of these old fuse boxes then the rest of the electrical installation has either outgrown its original intended use or has been fiddled with as number of times over 30 years such that it has become a hazard in places anyway.
If you have one of these old fuse boxes and want to refurbish a kitchen or bathroom, then it very likely it sensibly should be changed at the same time anyway.
Having said that, if a home owner has only budget for either a full electrical inspection or a new Consumer Unit, but not both. Then certainly I would recommend having the inspection done as the priority.