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Let me take a look at this and I'll get back to you in a bit.
Only those working on a self-employed basis in the construction industry need to register with the HMRC Construction Industry Scheme. It would be highly unusual if your father worked for a company of which he is a director on a self-employed basis and HMRC would raise an eyebrow too. The company should register as a contractor within the CIS (see here) and also as an employer (see here).
Your uncle could pay himself a low salary to avoid paying NIC and draw a dividend as extra income as profits allow. Any other people who are on the payroll would not need to be registered under the CIS. Only the sub-contractors working on a self-employed basis would need to be paid on the CIS basis.
I hope this helps but let me know if you have any further questions.
You can be self-employed and employed as a director at the same time but I see no point in your uncle working for his company on a self-employed basis. There would be no point in having a limited company. He could use subbies if he was self-employed. The point of the CIS scheme is to catch those who are not employees/directors.
If the company had an employee dealing with admin etc for example, they would not need to be CIS registered.