GrannyGravy13- and yes, it is the system here where I live currently. Everyone has to have Health and accident insurance by Law- and there are many (all private) to choose from. It can cost from about £400 each per person, and an awful lot more, depending on the deductible you pick and any top up for private care. Depending on the deductible, you have to pay that amount first before insurance pays, then you pay 10% of your bills yourself too, up to about £600 per year. For a family, it amounts to a huge sum, and many people with tight budgets don't go, as hey don't have the money for the deductible and the 10%.
In the UK, you know that private insurance won't take you if you have severe illness, handicap or pre-exisiting conditions. The Swiss basic system cannot refuse you, even with the above - but they will refuse you for any top up above basic care.