I'm not a Brit, but an Irish friend of mine told me that since redheads were "lively", they call them gingers because the spice ginger is used to "liven" up a meal. He's 74 years old, so this goes way back, according to him.
Not to hijack, but I also have an Ask a Brit question:
What do you mean when you ask someone "what are you having for tea"? Is it lunch??