In law a bicycle is NOT a 'mechanically propelled vehicle', so the rules applying to motorists don't apply to cyclists.
However, in law, a bicycle IS a 'carriage'. So the provisions of the Licensing Act 1872 (as amended) apply:
"Every person who is drunk while in charge on any highway or other public place of any carriage, horse, cattle, or steam engine, or who is drunk when in possession of any loaded firearms, may be apprehended, and shall be liable to a penalty not exceeding forty shillings, or in the discretion of the court to imprisonment for any term not exceeding one month"
Also, the Road Traffic Act 1988 states:
"A person who, when riding a cycle on a road or other public place, is unfit to ride through drink or drugs (that is to say, is under the influence of drink or a drug to such an extent as to be incapable of having proper control of the cycle) is guilty of an offence". (Sorry, I can't find the penalties which could apply).
However you can't ban someone from riding a bike, as that would (apparently) be an infringement of their human rights:
http://www.mirror.co....ight-115875-22145813/
Chris