Notice period if no contract?

[Fakerecords]

I'll have been there 4 weeks on Friday, it's a zero hours contract. I still haven't been given a contract as they haven't got round to it yet even though I've asked. They are also late in paying us, it was meant to be Friday, been told it 'should be tomorrow' now, which I'm sure is illegal.
I don't enjoy the job really, and I don't feel that I'm liked there.
I really don't know if I should wait and see if it gets better, but if not, would I be able to just give one week's notice given I've been there less than a month and no contract?

Surely zero hours cuts both ways. Are you signed up for a specific set of hours for next week? I'd walk.

Get all your pay first and then just leave.
I wouldn't even bother telling them.
Just don't show up any more.
Fuck 'em.

If they can't pay you on time and give you a contract, then they deserve nothing better.

It's in teaching. In my first few weeks I've been given a timetable, though I was told it would be changing this coming week. However I've no idea what it will be yet.
I've found with some zero hours jobs in the past that they only want the benefits of zero hours on their side, they don't want employees to exercise them .

Makes no difference.
No pay = now work.

"makes no difference" in relation to teaching - sorry not v clear in my post.

Luckily I've already got other 0 hours work I can do so wouldn't be without a job

Can you manage until the end of the school term?

It's a private language school, open all summer.