It's true that when naming the letters of the alphabet, the British call the letter Z, "Zed". But in both British and American English, the phoneme "z" /'zi:/, is pronounced differently from a soft "c" /'si:/.
Your native dialect may not have a phoneme similar to the English /'zi:/, but you certainly have the sound. If you've ever had your hair cut with an electric hair trimmer, then you've heard the English /'zi:/ --- "buzzzzzzzzz".
A "soft c" (/'si:/) in English is pronounced like the English "s". It sounds like air escaping a punctured tire, and that's basically how you make the sound. To make a soft /c/ -- hold your mouth slightly open, press your tongue to the roof of your mouth, with the tip against your upper front teeth, so that you can not exhale through your mouth. Now drop the tip of your tongue to let air escape, and finally feel your throat just below your jaw - if your vocal cords are not vibrating, that's an English /'si:/
To voice an English "z" (/'zi:/), hold your tongue similar to /'si:/, but drop the tip of your tongue to touch your lower front teeth. The big difference is the "voiced" part - when you exhale, the vocal cords vibrate (remember the electric hair trimmer :-).
The key is the vibrating vocal cords. Hold your fingers to your throat, when you practice -- vibrating = /'zi:/ ("fuzzy") --- not vibrating = /'si:/ ("fussy").
Some people soften their z's, so that they almost sound like a /'si:/. But remember those electric hair trimmers and you'll be buzzzzzzing away in no time.