Advice on SSP is all correct - self certify if under a week, but she will need to check out re. returning to work as she is in the food industry.
Re: contracts - if she turns up for work every day and she is getting paid then this is deemed as a contract - unless the employer is large, they vary rarely subsidise SSP. If the employer is a 'small business' which I imagine it is then they will claim the SSP paid to your mum back through their monthly Tax/NI payments to the tax office.
If your mum is getting 'cash in hand' for her work, then unfortunately she won't get any SSP.