Oh yes, the Swiss are great travellers- and yes, you got it right Calli- Swiss and Swiss residents, incl. British expats (and there are very many here, just not many in our region) have to have Private Health and Accident insurance, by Law. And that covers them worlwide automatically.
We however, have an excemption- as we are British retirees on UK pensions only, having paid into the UK system all our lives. This exemption is via Form S1- which will continue to give us cover both in Switzerland (we have to pay about £250 before it kicks in, per year, then 10% up to about £800- then free) - and also access to NHS in UK.
But this will not give us any cover in the EU after 12.20- and there is nothing here to replace it. There is no 'holiday insurance' that will cover us- as 99.99% of the population is covered- so there is no need for the vast majority of the population, and until 12.20- no need for us either. Nothing to do with human rights !
So, the only way to get insurance to travel- would be to rejoin the full Health/accident Insurance we had before official retirement age- at VERY expensive cost (as said, about £500 per month per person) and sort of pay 'twice'. Unless we can persuade an insurer to invent a new insurance product for the few, like us, in this position. As said, I don't know a single expat who is- and we are probably a very small number. All British expats I know who are retired here, worked in Switzerland for many years before retirement, and are not able to access S1 exemption, are on VERY fat Swiss pensions, and covered by their Swiss insurance scheme.