grey hair does not exist, it white hair mixed with coloured hair which gives the appearance of grey hair.
Nothing you can do but dye it, and reduce alcohol comsumption. Alcohol interferes with the absorption of a vitamin B complex which is linked to hair colour.

One of the reasons it looks fake is likely the chemicals in the dyes that are designed to supress color first (or simply strip it with peroxide) and then add the actual dye color. On greys, this means a) a really bright dye color and b) your whole head turns the exact same color rather than varying shades and highlights.

Something you may want to try is an all natural dye that has it's color base in henna or coffee or ink. I know Lush hair dyes do a great job.