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Are Visa/Mastercard/AmEx (UK issued) widely accepted in Switzerland?
Yes, stores that accept credit cards will accept foreign credit cards as well. Somtimes AmEx cards (no matter if domestic or foreign) were not accepted because of their vendor fees, but recently this seems to have gotten better, so if you only have an "exotic" card like Diners Club, JCB and the like, you may want to carry a more "common" card as backup.
Can I buy train tickets using those cards?
If you want to be sure, buy your tickets at a counter or a ticket machine, especially since you can easily buy return tickets or tickets to be validated at a later date. Also, pretty much all public transport in Switzerland are in a fare system, so a ticket counter can sell you tickets for any connection between two public transport stops in Switzerland.
How popular is card usage, aka. is it necessary to carry cash?
Cash is still king, see Bloomberg, so some smaller stores/restaurants might not accept cards at all, some stores (discounters) only debit cards like Maestro (MasterCard) and occasionally V Pay (Visa), but generally you will not have problems paying by card in Switzerland with contactless payments getting more and more widespread.
If you carry cash, breaking large bills (CHF 200, CHF 100) during purchases is not a problem, ATMs will accept international cards and dispense you any denomination starting from CHF 20/CHF 50.
Source: Ticket office clerk at a major Swiss public transport company