I know people who lost their liscense for riding their bikes while drunk. Rightfully so, luckily in my younger years I was never cought the few times I did so myself.
In the UK, drunk cycling is an offence with a maximum (but not usual) penalty of £2500, but you can’t be forced to take a blood alcohol level breath or urine test as a cyclist… so you’ll just get a charge of reckless cycling instead. Neither drunk or reckless cycling has any effect on your driving license.
So basically, as long as you’re not so impaired you’re an obvious danger to others you’ll probably get away with it, which might explain why it’s such a popular alternative to getting home from the pub.