In law a bicycle is defined as a carriage for use on the highway but cyclists are not in charge of 'mechanically propelled' vehicles so, in law, do not have to adhere to exactly the same rules as motorists, including 'drink drive' rules.
Section 30 Road Traffic Act 1988 says: "It is an offence for a person to ride a cycle on a road or other public place when unfit to ride through drink or drugs - that is to say - is under the influence of a drink or a drug to such an extent as to be incapable of having proper control of the cycle.
You can not get endorsements on your UK driving licence for a 'drink cycling' offence, however you can be fined up to £2500 for cycling dangerously.
I remember a story about someone being drunk in charge of a horse a little while back.