To the OP - you say that she "needs the P60 for tax credits". Well this is not strictly true. She has to declare her income, and the declaration form states that she can get the information from the P60. But provided that she has the INFORMATION which would normally be recorded on a P60 (ie payslips) then she should have enough information to fulfil the tax credits compliance.
I have to agree with the other respondents that on the face of it her working conditions appear to breach employment law, but that is another matter. I have to say that it is not that unusual in the hotel trade.
On the PAYE front I sort of have some sympathy with the employer, if he was first provided with a P46 and then later, no doubt after the year end and possibly after he has completed the annual PAYE returns, gets handed a P45.
That said, if she was paid at above the lower earnings threshold (almost certain if not in breach of National Minimum Wage regs and if the individual qualifies for tax credits) then even if there were no deductions there would still be an obligation to file a P14 with HMRC and provide the employee with a P60 (the statutory deadline being 31 May, by the way, so still in time).