Is this safe to leave wiring on show from fuse boxes

As long as the cables are undamaged this fine not best practice but fine. Sound like an old installation.

Providing there is no inner sheathing (colour wires or bare copper) showing it should be fine and wouldn’t have an adverse effect on the overall safety of the installation. Best practice would be to enclose the cabling within a containment system such as trunking and to ensure Ingress protection is adhered to by correct entry to the consumer unit.

Both answers you have received are great advice. I will just add that it is not uncommon to clip cables directly to the walls, just like you will have a cable showing between a light pendent and ceiling rose. As long as the cables are not damaged and you are not able to access the inside the fuze box where the cables come out (poking around the gland with a screwdriver or finger), then the fuze box is sufficiently secure. If the cables showing are the actual power cables form your energy supplier to your fuze box, then I would probably get someone to look at fire rated casing to make sure you don't damage those moving furniture etc... Hope this helps. Nico

Ideally cables should be covered with trunking, conduits or cables caps where possible but if risk assessment has been carried out prior to installation then I believe cables have mechanical protection and also protected by RCD or RCBOS or cables are out of reach. But if cables are showing exposed wires then immediate remedial work needs to be carried out. This means cables insulation has been damaged or deteriorated.