There are a number of acts of parliament which cover dogs and their owners. A summary of some of the relevant acts and regulations are detailed below, as well as a link to the relevant act/regulation in full (if available).

Note This list is not exhaustive, but I think that all dog owners will find the details below enlightening.

The Control of Dogs Order 1992

This order describes the requirement that all dogs on the highway on in a public place must wear a collar and have an identity tag or plate which gives the owner's name and address.
Note: Just your telephone number is not sufficient.
There are some exceptions to this order - mainly relating to working dogs, but the owner must have the proof of lawful authority on him.
This order gives the local authority powers to treat such a dog as a stray. (Note does not empower the police)
For further details see The Control of Dogs Order 1992

The Road Traffic Act 1988

Section 27 of the Road Traffic Act 1998 states that:
"A person who causes or permits a dog to be on a designated road without the dog being held on a lead is guilty of an offence. It also states, in this section, "designated road" means a length of road specified by an order in that behalf of the local authority in whose area the length of road is situated
For further details see The Road Traffic Act 1998

The Environmental Protection (Stray Dogs) Regulations 1992

These Regulations implement certain provisions of the Environmental Protection Act 1990 with regard to stray dogs.

The Regulations state that the local authority must appoint an officer for dealing with stray dogs found in the authority's area. An owner wishing to reclaim a dog which has strayed, can only do so if he or she pays the authority's expenses incurred by detaining the dog, together with a fine. The fine amount is currently set at £25.

The Regulations also oblige the officer to keep a register of dogs seized by him or her, and the details that are to be entered in the register. The register must be available for public inspection. The Regulations also describe the procedure to be followed by the officer where a dog is found by a member of the public who wishes to keep it.

The Environmental Protection (Stray Dogs) Regulations 1992

Dangerous Dogs Act 1991

This act applies to all dogs, not just "fighting dogs"* and owners should be aware of its contents. The act applies to any dog deemed to be dangerously out of control in a public place. The penalty for having such a dog is either destruction of the dog or the owner may be disqualified from owning a dog for any time the court sees fit.

For further information see Dangerous Dogs Act 1991

^*Under the terms of the act a "fighting dog" is described as one of the following:-

1. Pit Bull Terrier (also crossbred pit bulls)
2. Japanese Tosa
3. "any dog of any type designated for the purposes of this section by an order of the Secretary of State, being a type appearing to him to be bred for fighting or to have the characteristics of a type bred for that purpose."