The standard of healthcare that you can expect in Switzerland is as high as anywhere else in the world, and provided you have an E111 form, medical treatment in hospitals will be provided at no cost.
The E111 is not a substitute for taking out actual Travel Insurance, and you should make sure that you have cover arranged prior to travel to pay for things that are not covered by E111, such as air ambulance extraction from remote areas, or medical evacuation to the UK.
If you are planning to go mountaineering in Switerland, you may need to take out additional cover due to the risks involved.
