Im an electrical installations student, but thought i'd answer. Old fuse boxes may not have been rated to cope with the electrical load that you may now require, but all kitchen appliances should be earthed, dishwashers, washing machines, cookers etc, A new fuse box will have an RCD (Residual Current Device) to detect current to earth faults, and are designed to protect you from electrocution. Also a Part P registered electrician (which they should be to change the comsumer unit) is legally responsible for the installation.
ok first you must have an earth in your fuse box ,but you should also have an rcd .If your DB (fuse board ) is an old type ,fuse wire it should be replaced some of the early fuse boxes have a wooden frame round the base if you have a fault within the board this could catch fire !!! ,if your DB is replaced it should be a modern type withMCB's oh and youll need your water and any other service ie Gas oil earthed as well and also supplimentary bonding where required ,if they replace the DB make sure they are NIC or ECA approve and are registered part p ,they must provide you with an installation certificate and advise building control at the local council ,may be worth contacting a reputable electrical contractor for advise or ask them for a periodic inspection ,this will show any deviations to the regulations and defects within the installation
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