Yes, they certainly could, which is appropriate for the following reasons.

. Alleviating a heavy load on the fuse box on these is never a bad thing, given it's overloaded as standard.
. The wiring at best is 25+ years old, during which time it would have built resistance, which may be a reason why you have the issue you have.

This is why I suggested rewiring independently, as what the garage are proposing (i.e. replacing the fusebox) is a major/costly undertaking.

Martin