A couple of years ago, mate of mine was set to ping in a shitty email having already accepted a new job offer starting in two weeks (one months notice)…
I talked him down and persuaded him to write a letter, and not burn too many bridges.
Basically we (tactfully) put the case to his line manager that, he was currently without a project to work on (or much motivation), and that allowing him to leave at the end of the week, burn up his remaining Holiday hours and then leave would benefit everyone, The line manager went one better and got him to clear his desk before the end of the day…
Don’t complain or bitch about the company, claim to have “Enjoyed your time” spent working there. Then present a reasoned case as to why being allowed to not work your entire notice period will be of mutual benefit to yourself and the company…
Be prepared to sit down and discuss it once the letter is presented and have your diplomatic answers ready…