If your Fuseboard has fuses with fuse wire in them, then in my opinion yes it’s time to upgrade/replace your Fuseboard. To comply with the latest regulations (17th edition bs7671), all cables buried in a wall less than 50mm from the surface, need Rcd protection. An Rcd is a special device that is in new Fuseboards, that trips out in milliseconds to prevent electric shock, it basically monitors the circuits it’s connected to for any faults, and when it detects an earth fault, it trips within a certain time in milliseconds.
For example, if you were putting a picture up and hammering the nail into the wall, and you were to go through a cable that was buried in the wall, the Rcd would trip out at the Fuseboard saving you from getting a nasty shock; alternatively if you had an old style Fuseboard with No Rcd and nailed through a cable, it could take a lot longer to blow the fuse, a few seconds which could make all the difference.
So for peace of mind and safety first, I would recommend you consider upgrading to make the electrics in your home a lot safer for continued use.