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Contractoruk is my goto for this sort of thing
https://www.contractoruk.com/contracts/what_fixed_term_contract.html
From the look of it, if the contract is between the Co. and the Ltd, it's not an FTC. There is no employment contract and not responsibility for the Co. to pay sick leave or pension and the like.
As a director of the Ltd, it's up to you how you pay you the employee of the Ltd, including hikiday oay / sick pay. My Ltd, for example, paid me a monthly salary, irrespective of holidays or sickness.
Your Ltd can even pay gross into a pension for the employees, and save on NI payments, and corp tax.
FTC invoicing through a Ltd Co. Are you eligible for sick/holiday pay and pension or do you need to be PAYE for those?