When you're self employed you get paid gross i.e. all the money agrees in the contract is paid to you, then paying tax on all your earnings to HMRC is for you to sort out.
Here's an example:
Let's say IACGMOOH pays KP £200,000 for one series.
Of that, the first £50.270 will be taxed at 20% = £10,054.
Between £50,270 and £125,140 will be taxed at 40% = £74,870 x 40% = £29,948
Anything over £125,140 will be taxed at 45% = £74,860 x 45% = £33,687
So from a £200,000 payday, KP should have held back £10,054 + £29,948 + £33,687 = £73,689 to pay in tax
She would also have to pay NI:
6% for earnings up to £50,270 = £3,016.20
2% for earnings over £50,270 = £149,730 x 2% = £2,994,60
NI total = £3,016.20 + £2,994.60 = £6,010.80
So KP should have held back £74k + £6k = £80k for Tax and NI
My numbers are probably slightly out, but it would mean of the £200k earned, KP would only have £120k to spend on staff and her family expenditure. I'm guessing she spent much more than that, looking at her lifestyle.
I suspect she had an accountant to tell her all that this, but unless she provided the accountant with the cash to pay HMRC, the accountant would not have been able to pay the bill to HMRC.
On these kind of sums, fines and penalties rack up very very quickly.