The main Smiddy families originated in Ireland around the area of Co.Cork. Unless you know that your family originated from England you should start with the Irish Families.
I have been researching my Family of Irish Smiddys and have designed a web-site on my family a book on the Irish Smiddy Family was published 2 yrs ago.
It is http://asmid69.pwp.blueyonder.co.uk
if you would like a look.Feel free to post info. re. your family and I will try to link it to what I know.