All Mod Cons

I don't have a feed and expansion tank, however i do have shower mixer that takes water from the hot water tank, however I think the cold comes from the cold water tank rather than the mains supply. Do you think the problem could be there?

I wondered if the coil inside the hot water tank could be perforated and then water inside the tank could be feeding (under pressure) back into the hot water system pipes. Do you think this is a possibility?
thanks.