At work we have just moved into a new building. The cold water tap has hot water coming out of it every morning, it does run cold after about 30 secs but I am concerned about the risk of picking up le4gionella or something. Should I be worried?

Probably not. The CW pipe probably sits next to a boiler pipe supplying HW. Legionella rarely come from the drinking water, it is airborne and comes from water sitting in evaporator trays or cooling towers. The bacteria finds a nice warm home and grows there. Utility supplied water is treated with chlorine or UV light and is not usually a point source.