Your zero hour contract doesn't matter it's what you actually got paid in your qualifying weeks. If you don't qualify for SMP then you may qualify for Maternity Allowance which is very similar but doesn't have the six week enhancement and is technically classed as a benefit.
Your employer has to give you a specific form if you do not qualify for SMP outlining why. You then use this to claim MA.
In the event you don't qualify for MA I understand you can apply for Employment and support allowance.
I'll post a link for you to check your qualifying levels in a mo but as a rule of thumb if you were employed before you became pregnant and earn enough each week to pay NI contributions you're probably fine for SMP.
I had a quick look at your link and it appears to confirm what I said Flowery although I'm happy to be corrected if I'm wrong. We're only human after all
The link states it's only the self employed who are definitely not entitled to SMP. It doesn't appear to overtly cite the woman's employment status beyond the woman must have an employer and cannot be self-employed. So that would mean a worker can be eligible so long as they meet the service and earning requirements.
This is interesting. The technical guidance definitely says SMP is for employees, and mentions continuous employment, and employer, several times. You are right it doesn't specifically say that casual workers are excluded.
Then in the link you previously posted, the one about how different employment types affect it, there is a section on "Casual and short contract employees" which the guidance defines as follows: "A casual employee is usually someone who works for an employer, as and when they are required on a series of short contracts of employment with that person"
True casual workers, with worker status rather than employment status, with no mutuality of obligation and a genuine casual agreement, aren't employees and don't work on short 'contracts of employment'.
But that doesn't exactly answer the question does it? So I don't know! I don't think it's correct to say it literally makes no difference, I think if a genuinely casual worker might be entitled to SMP it certainly won't be as clear cut as an employee who meets the 26 weeks continuous employment plus earnings requirement.
I would still be interested to know whether the OP is a genuinely casual worker or whether she is an employee who happens to have zero hours in her contract, and either way, her employer is not correct to say that zero hours= no SMP, clearly it's not that simple at all, whether it's zero hours employment or a casual ad hoc, work a few-hours-every-couple-of-months type arrangement.
My understanding is that the law requires you to be an "employee" to qualify for SMP. However, "employee" has a wider scope than the typical and I would imagine could cover zero hours workers (as it covers agency workers). If you are a typical taxpayer and NI payer through payroll then you're likely to be covered.
You don't qualify for maternity leave, though, just pay (arguably). But they may still need to provide you with 39 weeks pay, assuming that you qualify.