Arrange a meeting/video call with your boss. Tell them you've been offered a new job and will be resigning. After the meeting, give them (or email if working remotely) your official letter of resignation - check Google if you need examples or templates. Check your contract to see how much notice you're required to give - it might be 2 weeks, but more likely 4. You'll probably work out your last day with HR. Work your notice period, then on that last day give back anything you need to, say "thanks for everything" and walk off into the sunset.

You don't really need to do much in the way of "legal/tax stuff" - most of this will be taken care of by your current employer, new employer and HMRC. It's helpful to get your P45 form from your current employer when you leave; they might send this in the post a few weeks after your last day. Give this to your new employer so that they put you on the correct tax code and you pay the right amount of tax when you start in your new job.

That's about it.