Insurance applications are always traps for the unwary. When you apply through an agent, the agent is normally deemed to act for you and any misrepresentations are thus attributable to you.
Status as a student does not change domicile nor, arguably "permanent residence". But unlike domicile (well actually domicile does have multiple meanings especially as between different legal systems) "residence" has no fixed meaning for different purposes.
And the UK Post Office, which offers (I'm reliably told) the best travel insurance, does not offer it to nonresidents: http://www.postoffice.co.uk/portal/p...00735#43200274
Best advice: explain your status. If you have Swiss health insurance, even if you have a British EHIC card, you are probably covered by a Swiss travel policy bought in good faith. But if you state that you are a British student resident in Switzerland for X months for purposes of study, the insurer cannot later say it was misled. (Travel cover sold in most countries takes account of domestic health cover; so, for example, a UK policy will reserve the insurer's right to repatriate you to the UK and leave you in the care of the NHS. That may be the reason for the UK Post Office's rule on residence, and it may be that the rule is simply infelicitously drafted as regards students -- but you are stuck with it.)
Your nationality (British) has little relevance to the case except insofar as the Swiss seem to obsess over such things. (I say this because, whenever I approach officialdom in connection, say, with something to do with my British wife, presentation of my Swiss ID card seems to alter attitudes. My French accent is "international"; I studied in Belgium.)
Note that "misrepresentation", minor or major, relevant or not to the risk, has different effects in different countries. In England/Scotland it can vitiate the cover. In Germany relevance is the key. In France the recovery is reduced proportionately to what the premium ought to have been. I haven't ever had occasion to inquire as to the Swiss rule.
Finally, this Web site http://www.goldencare.ch/ avers that it will insure Swiss nationals or foreigners, including students, regardless of status.
(The best health insurance -- such as that offered to UN employees, including those who retire in Switzerland, and which is acceptable as health cover under Swiss law http://www.eda.admin.ch/eda/fr/home/...ns/inshea.html -- makes travel health cover redundant in most respects. However such policies don't (or don't usually) pay for repatriation. And a stretcher evacuation can mean paying for as many as 9 seats. Or worse, in the case of a private plane. Whether you need the other aspects of travel cover -- loss and theft mainly -- depend on what other insurance you have and what your credit card issuer offers.)