Both moths and silverfish live and breed in cool and damp places.
Moths lay their eggs close to some material suitable for food. When the eggs hatch, it is the larvae not the moth, which eats the clothing etc.
Silverfish eat almost anything including paper, book bindings, wallpaper and clothing.
What you can do
Store clothing in sealed plastic bags during summer and make sure they are clean before storing away as soiled cloths and perspiration attracts the pests.
Don’t keep old newspapers stacked on floors as this will attract silverfish.