Fareaster is writing drivel. UK based crews spending more than 90 days a year in the UK have always been liable to UK tax, but if their company has been based overseas they have not paid National Insurance. The only change, demanded by the Treasury, is that the company collect the tax due rather than leave it to the individual. The individual will be given a tax code and the company will collect the tax according to the tax code.
Those who work for CX in the UK but live outside the UK will also receive a tax code but theirs will be a no-tax code, which means the company will not have to collect any tax from them. In the case of UK domiciled crews, i.e. Uk passport holders, they may have to furnish proof of their overseas address or otherwise prove that they spend less than 90 days a year in the UK. In the case of non-domiciled crews holding foreign passports, a no-tax code will probably be automatic.
Domiciled refers to the country whose passport you hold. Resident refers to where you live. If you live on a boat and spend less than the minimum days in any country, you are not resident anywhere. You are not required to be resident anywhere, but you will still have a domicile.
If CX set up an onshore company, both CX and their crews will become liable for National Insurance. NI will not apply to foreign domiciled crews living overseas, but will apply to UK residents and UK domiciled crews, even those living overseas, although the latter will still pay no tax. If CX were faced with setting up a UK company and paying NI, I suspect they would reduce the manning levels in the UK to a minimum and move crews to other bases. Positioning crews around would be cheaper than NI for CX.