Does my dog need to wear a dog tag?

Yes. The dog tag law UK states that all dogs (with some working dog exemptions) are required to wear a dog identity tag or other form of clear identification by law. 

The Control of Dogs Order 1992 mandates that any dog in a public place must wear a collar with the owner's name (initial and surname), address and postcode engraved or written on it, or engraved on a dog identity tag. 

You are legally required to put your name and address on your dog's tag. A house number and postcode are all that is needed to specify an entire UK address, so it is perfectly acceptable to put just those details and your name. This can be useful for smaller tags where there might not be space for your full address.

we would strongly advise also adding at least one contact phone number even though it is not required by law.

What happens if my dog does not wear an ID tag?

You can be fined up to £5,000 if your dog does not wear a dog identification tag or the tag does not have the required information on it.

The Control of Dogs Order 1992, the law that states that dogs should not be in public places without the owner's name and address information, actually states:

"Every dog while in a highway or in a place of public resort shall wear a collar with the name and address of the owner inscribed on the collar or on a plate or badge attached to it."

Is my dog exempt?

Probably not but there are some exemptions.

Dog identification laws do not apply to:

any pack of hounds (by this they mean hunting animals)

any dog while being used for sporting purposes

any dog while being used for the capture or destruction of vermin

any dog while being used for the driving or tending of cattle or sheep

any dog while being used on official duties by a member of Her Majesty’s Armed Forces or Her Majesty's Customs and Excise or the police force for any area

any dog while being used in emergency rescue work

any dog registered with the Guide Dogs for the Blind Association