So, if he's employed by a UK company, under UK PAYE, then he's under the remit of CMS. They will assess his earnings no differently than if he was on PAYE at Superdrug.
If he's on the payroll of a non UK company, then he will pay tax at source in that company, but as a UK resident, he needs to declare this on a UK tax return. He will fall under something called double taxation relief, which essentially means, he puts £100k of foreign income on his tax return, and his UK tax is wiped out because he can counterbalance the UK tax calculated with what he's paid abroad. No tax to pay. But a UK tax return, fully assessable by CMS.
If he's a sole trader (unlikely) or a limited company and set himself up so he invoices people for work done, then he also should be putting this on a UK tax return.
Does he rent or own a permanent property in the UK? He'll do well to claim he's got no residency here if he has. And he needs to submit a return.
If he's a twat and doesn't submit his tax returns, so the CMS can't see any income, then you call your MP and get the financial investigation unit involved. Who will access all his accounts, and see any money coming in. Then they will force him to attend an interview. When they see this is what should be on a tax return, they will inform HMRC, and do a calculation on his income, as if they had seen it.
Sources: I am a qualified accountant, and have just spent the last 4 years battling my twat of an ex doing the exact same thing. On an overseas payroll. Hasn't done a tax return since 2016. CMS can't assess what they can't see. MP got the FIU to do a full investigation. They hauled him in and presented him with a copy of the deeds to his house and his mortgage and all his bank statements (he was pretending not to be UK resident as well) and backdated the last 4 years of CMS to me on the large salary he was receiving in Euros.
Fucking idiot men stooping to any level to deny their child the support they need.