Unless the wiring is very old or has faults it will be possible to just upgrade the fuseboard. Each circuit can be tested before or during this process. Get some quotes from electricians registered with one of the Part P schemes
Call a electrician and ask for a quote, an experienced electrician will make a visit and offer the alternatives to you. Depending on the age and condition of the installation.
As part of a board change a full electrical installation certificate will be issued entailing all of the installation to be tested.
An electrician would need to make a judgement on the age, condition and safety of the current wiring prior to changing the fuseboard. Any works required to bring the installation up to an acceptable standard should be quoted for and completed along with the fuseboard upgrade.