Only magistrates and juries are empowered to legally determine whether someone is guilty of an offence or not. The police have no powers to do so. Even if your action had been witnessed by a capacity crowd at Wembley Stadium, and been shown live on national TV, they'd have no right to take any actions based upon a presumption of your guilt. Nothing can happen until either you've admitted your guilt or been you've found guilty by a court.
(If you think about it, that's the only sensible way to do things. Otherwise someone who didn't like you could get together with their mates to say that they'd witnessed you committing an offence while you were drunk, and get you cautioned as a result of it).
So you can only be cautioned if you admit to the offence. If you don't, the matter will be handed to the CPS. It's possible that the CPS might decide that it's not in the public interest to pursue a conviction, but it's still quite likely that they'd would do so. Assuming that you pleaded guilty, a conviction would probably result in a 12 month conditional discharge, plus the payment of costs (perhaps �60) and a 'victim surcharge' of �15. If you pleaded not guilty the conditional discharge would probably be replaced by a fine (of perhaps �80).
Chris