I write sometimes on this issue.
It is unusual to be dual-tax-resident in the UK and Switzerland, but it does happen. It is possible to appeal under the Tax Treaty against the effects of that, but not always worthwhile. Often the issue can be resolved administratively. See, for example: http://www.hmrc.gov.uk/manuals/dtmanual/DT18153.htm
On both a theoretical and practical basis, the most important conflict, at least of high-net-worth individuals, is the Swiss wealth-tax component of Confederation, Cantonal and Communal tax: there is no credit against this against UK tax. And of course British income and consumption tax rates reflect this (they may be higher).
There is a Social Security (i.e. AVS/NIC) Totalisation Agreement (double contribution agreement) https://www.gov.uk/national-insurance-if-you-go-abroad . You need not pay contributions to both unless you choose to do so: this would normally help the low-paid and certain self-employed individuals and perhaps some persons on the threshold of retirement. If you are subject to NIC (not likely if you are only going to be dual-resident for a few years, as there is (I'm not looking it up to confirm, but most Totalisation Agreements have such clauses) a provision that those in the UK for only a few years continue to pay into the other country's system. (Just as well, since State Pension isn't normally payable if you don't have 10 years' credits -- and parenthetically every British person should use one of the (several) workarounds to try to get 30 years of credits since it's a cheap investment for a decent payout. Voluntary Class 3 is the most expensive -- £722.80 -- see the alternatives: https://www.gov.uk/personal-tax/national-insurance ) If you pay NICs as an employee of a foreign non-resident company you will probably be exempted from the employer's portion of the NICs: that's a gift to certain such workers, and to employees in Britain of foreign governments.
British taxation is, for those with significant non-wage earnings, by self-assessment. Your Swiss earnings may fit on form SA106 https://www.gov.uk/government/public...-foreign-sa106
It is wildly improbable that your Swiss employer will be deemed tax-resident as a corporation simply because you are working in the UK. The question is whether the firm is "doing business" in the UK, and that's a complicated issue. Having a local representative is not, by itself, enough to make a foreign firm taxable. Does it actively market in the UK, and have UK customers? Does it have a "permanent establishment" (a term of art) in the UK?
Your Swiss employer does NOT need to, and should not (although he can, but it will cost him and he'd lose the exemption from employer share of NIC) register for PAYE. You can be taxed as if you were self-employed, paying instalments to HMRC (probably after your first SA100 self-assessment return.) You'd be billed for your first year's tax in arrears.
Despite spending more than 90 days in the UK you might not be resident. It all depends. https://www.gov.uk/government/public...-tax-liability I think this is especially true if your long stay is only in one particular year. Think of "ordinary residence" as well as "residence". Of course you've only been away 2 years so HMRC will tend to think of you as a returning resident.
Filing Swiss taxes despite being based abroad is easy. You need to decide whether you want to remove yourself from Swiss taxation and onto British taxation. You haven't provided enough information for me to give you any opinion. What does your Mandataire fiscal / Begriff Bevollmächtigter say?
Sorry, the above isn't legal advice, just some things that came to mind as I ready your query.