secure (or not) websites

You can call, you can email, you can use their website - secure or not. The "risks" are all the same - that someone on their end will pass credit card information along to a thief. The method you send the information is of miniscule risk. Same risk applies at a restaurant when you hand over your card to the waiter and they "disappear" with it to process it. Besides, what is you real risk? If your card is compromised, you are liable for no more than $50 (if even that). Sure it's a pain to get a new card and change automatic payment accounts, but that's it. We always recommend to have a backup card when traveling and to notify your card-issuer now so they know you are making these reservations.

Same risk applies at a restaurant when you hand over your card to the waiter and they "disappear" with it to process it. Since skimming became noticed in the UK and since Chip and Pin was introduced with the small portable, often wireless, devices for entry of the PIN, it is extremely rare for any operatives to attempt to disappear with cards. The Chip reader pads are either handed to the customer or are at point of sale at a comfortable height for the entry of PINs. There are usually signs directing customers to cover their entry with the other hand or something else to prevent shoulder surfing or skimming. There is no way you can tell if somebody is talking on a mobile phone. Mobile numbers in the UK begin with 07, non-geographic ones begin with 08 or 05. Premium (adult content) and expensive support lines begin with 09. Normal land line phones begin with 01, or 02 or 03. But you still can't tell. I imagine it is the same in Brandon. A landline can be forwarded to a different number, and to a mobile. A mobile can be forwarded to a landline. And VOIP facilities like Skype can be used with any of those. It just comes down to trust.