He maybe attempting to do it because he believes it saves him money, but he is completely wrong. If you are earning below the NI threshold, there is no employer's NI for him to pay (and no employee's NI either - as I'm sure you know), so there is no saving.
You do have a contract of employment with the organisation (whether you have any bit of paper or not). He probably doesn't think you do. What he is attempting to do is dismiss you and re-engage you as self-employed. For starters, he can't just do that as a redundancy because the job clearly isn't redundant.
In addition, you would not be not self-employed based on the terms you have described the job - to be so, you would have to have control over the hours you did and when you did them (this is but one of the tests HMRC uses). That can never be the way for pub work - you work when called upon and are paid by the hour - being self-employed implies you are paid a lump sum to complete a task of work. It's completely incompatible with any concept of being paid by the hour. The way organisations (who don't wish to take on permanent staff) would get around this is to have you employed by an agency - who then becomes your employer - but then any agency wants a cut, so I'm not suggesting this to you - merely pointing out how these things work.
I'd just go back and point out the above to him and try to elucidate what he thinks he is gaining.
Tora x3 answer is completely wrong, BTW, and it is a pity that people have have no knowledge of these things attempt to answer complex questions that are clearly beyond them.