The simple answer is that nothing changes in relation to the VAT. There is still a taxable supply of staff/services from the VAT registered personal services company to the employment agency. VAT is still calculated on the full value of the supply: no account is taken of any payroll deduction made.
In this case, the value of the supply is based on the daily rate. If the daily rate is £100, the value on which VAT is calculated will be £100, not £100 less any payroll deductions.
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