@Ohmnomnom
Why is it illegal for a retail shop to employ people on a self-employed basis, but not for companies like deliveroo, maid2clean, etc?
While the likes of Deliveroo etc like to argue that their workers are self employed, it's a bit of a grey area and not particularly fair on the workers, who take all the risk and often don't earn NMW. There have been court cases and appeals etc.
Workers are generally exploited in these types of businesses and there should be a lot more outrage about how badly they're treated, but customers like being able to tap an app and have takeaways magically appear at their door to care.
On the OP, that's outrageous and they're likely to be breaching tax and NMW law, because for the latter, your basic expectation is that you are paid NMW and get at least the minimum holiday allowance, pension contributions and if relevant, sick pay and statutory redundancy.
For you to be self employed, which you wouldn't be for shop work anyway, you'd need to be paid a substantially higher hourly rate to compensate for the lack of employment rights.
Perhaps call their bluff. Tell them that you agree to be self employed and your rate is £20 ph. Plus you won't be available during weeks A, B, C and D, any BHs or between Christmas and New Year because, as a SE person, you have elected to not work as those times, as is your right.