You can, of course, not turn up to work. But that might well make you "unreliable" if you ask for a reference later. But it's not a problem, since a new employer giving a three month notice period will expect you to be on one at present.
(The notice period during the first 6 or 12 months is often less, eg 2-4 weeks.)
E.g. in Norway it is near impossible to give less than 3 months notice for permanent positions without providing additional compensation, no matter how junior the position, except for a typically 6 month trial period.
Before I'd moved to the UK, I'd never even seen an employment contract with less than 3 months.
In practice, shorter notice is often mutually agreed on with or without compensation when both sides agree it suits them, but it's very common to serve out the full 3 months.