I'm an electrician, will I do?
Both previous answers are correct in that no-one can force you to upgrade a perfectly serviceable (and safe) Consumer Unit ("Fuse box" or CU) just because it has re-wireable fuses. However - if you have additional works done which involves adding new circuits/cables, then those works DO have to meet the current standards (BS7671:2008 17th Edition IEE wiring regulations and Part P of the Building Regulations).
Fuses and MCBs (miniature circuit breakers) both protect primarily against over current situations (if too much current is drawn then the fuse breaks or breaker trips) In addition we now have fault protection devices called RCD (Residual Current Devices) which look for live/earth or neutral/earth imbalances caused by faults and cut the supply to that circuit.
There are a couple of applicable parts of the current standards which apply in your case, 1) all circuits in special locations (kitchens, bathrooms, OUTSIDE) must have RCD protection to protect against fault conditions. 2) cables not buried at least 50mm in walls or having additional mechanical protection, by means of earthed conduit ,must have RCD protection. Your current CU doesn't offer this RCD protection and cannot be upgraded to include it - only replaced I'm afraid.
An electrician could add a separate CU, with MCBs and RCD protection, just to run the new outside light circuits, or change the old CU to a new one with MCBs and RCD protection for all circuits.
A separate small CU just for the new circuits would be around �35-45 including breakers and maybe half a day to fit at around �100-120 labour. Cont.........