Vet with CatI cannot stress too often the importance of ensuring your Cat and Dog has some form of identity.  An identity tag is better than nothing.  However, these can easily drop off. Therefore, microchipping really is the safest form of ensuring that should your pet be lost, whatever it is, it has a good chance of coming home.  Most rehoming and rescue centres now use scanning devices.
Unfortunately, or not, an animal cannot speak and has no way of informing anyone of its origins. The pet is lost, the owner is frantic with worry, the animal rescue centres are bursting at the seams.  I have helped out at two rescue centres and cannot believe that all the animals who end up there are all strays.  Unfortunately, there are so many rescue centres, that you cannot possibly contact them all and your beloved pet may have been rehomed before your search has really begun in earnest.
No-one wins, except the lucky person who now has your pet, everyone looses.  Do yourself the best favour you can as a Pet Lover, especially for pets who are not caged all the time, and contact your vet, or local animal rescue centre (who may do it cheaper) and have it microchipped.  It's one of the best investments you can make, especially bearing in mind that if a Dog Warden has found your dog and it is taken to their Dog Pound, the dog's first day's stay costs more than it does to microchip it in the first place, and costs keep mounting each extra day it is there for, usually 7 days, when it is then passed to a re-homing centre.
Cats and Dogs have to be microchipped as part of the "Passports for Pet" Scheme if they want to travel to MAFF approved countries and avoid quarantine on their return into the United Kingdom.
Passports for Pets Page
Vet with Dog