Rights to end broker agreement and cancel insurance

I signed an agreement with a broker to set up health insurance for my family and myself. We subsequently received a letter from the proposed insurer with details of the policy and a health declaration but nothing since. This was around two weeks ago. We have since gone to another company to buy a non-health related insurance who informed us that they had discovered through the canton that we are not actually insured. We were told that they could insure us and it is simple to cancel the previous broker agreement and any related policy. My question is therefore: is the information about our right to cancel true and more generally do we have a cooling off period to cancel any unwanted insurance? Thanks.

As far as I know, it isn't possible to cancel compulsory health insurance taken out through a broker once you've signed up . See this thread:

https://www.moneyland.ch/en/forum/cancelling-contracts-in-switzerland-2414

It can take some time to receive your policies when you sign up through a broker, so that may be why you haven't gotten them yet. If you received confirmation of acceptance though, that acts as a guarantee. To be safe though, just call the insurance company which you signed up with through the broker. They should be able to tell you straight away whether or not you are insured.