The 13% goes in employers NIC contributions.
Generally gross salary is taken on permie roles as including all other bits of tax. so give or take allowances (which I cannot be bothered to calculate)
For each £1000 you get on contract, £130 is taken off as employers NIC contributions. The remaining £870 is paid to you. unfortunately, Hector takes his cut, before you get it, but, for any benefit, or inland revenue purposes, your earnings were £870.
And yes I know there is a £100/week NIC free allowance, I just couldn't be bothered to do the sums!

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