ok seen that a few times in this thread, technically it is, under the Road Traffic Act 1988,it is a criminal offence to ride a bicycle on a road or public place while in an unfit state through drinking alcohol or taking drugs.
now fine you can argue a couple of pints wont impact your ability to safely control your bike and put you in an unfit state, so no offence is being commited, but unlike drink driving theres no specific limit to rely on (though the police can breathalyse you as a cyclist and it would stand as strong evidence for the offence being committed if you were over the drink drive limit) its a purely subjective test by the police who stop you, and their view may well be that a couple of pints is too many, or it might not.
so its worth remembering that, and for those that say ah but the police will never catch you, sure its unlikely, but there was a guy in our local pub the other week who cycles to the pub, who was complaining he got stopped by the police on the way home as "he was all over the road" and now has a court appearance, with a potential minimum £1000 fine, criminal record etc to worry about. now he drinks far far more than a couple of pints for sure per pub visit, and completely denies he was all over the road, but still I think he's going to struggle to contend it.