Thanks for your response. What I am currently not sure is how I shall proceed now? Am I allowed to bill the agency via my Swiss company? I understand the income my company receives is still different from my salary, so which cash flow will be liable for what tax? Say if my company bills the agency GBP 10000, and pays me only a low salary of say 1000 GBP per month while working in the UK, what income is taxable under UK law?
And if you say the DTA would stipulate that I can offset my total Swiss tax payable with the amount already paid in the UK, that wouldn't be too bad as it means I still only pay tax according to Swiss rates (which are considerably lower than the UK), and for me personally, I don't mind whether a proportion of that goes to the UK tax offices. Or am I missing something here?
By the way, regarding NIC, I would assume I can still stay under the Swiss system as I can second myself to the UK and provide the UK authorities with the respective proof (there is a so called form "A1" for this)?