How do I find out where my surname originates from?

Is there anywhere I can find out for free online or something where my surname originates from? I'm black, I live in England,.. but I know I have white Dutch (on my dads side), portuguese, and indian (on my mums) heritage somewhere down the line. The dutch side coming from quite a well off royal background who I think got one of his workers pregnant years and years ago. And either the mother of his child (previously the worker), or the child inherited the mansion after he died. That child I beleive would have been my grandads (now ped) father. I really would like to find out more about this. How can I??