What did you say to your colleagues? Do you have a HR team that you can talk to?
I'd go in and clarify with boss that you have not handed in notice and put in formal complaint that he has taken it as such and told other people. He has nothing in writing and if you have a contract I presume notice has to be in writing?. As far as I am aware (HR advice in previous job) even if you hand in your notice, you can 'take it back' at any time during your notice period.
Obviously none of that deals with the fact that your boss is a twat.
Sorry you are having to sort this out - if your boss is this much of a twat I would think about leaving sooner rather than later?
To be fair, you don't know that the boss blabbed - could be he's asked the powers-that-be and their PA has been asked to sort something out and she had lunch with your colleague... You know how workplaces are, hotbeds of gossip!!