Old thread, but it still comes up as the first hit. I think this is pretty accurate to the Shirley Collins version:

Am)As I go (C) a-walking down (Am) Birmingham (G)Street
(Am)In my new (C) scarlet jacket all (Am) neat and (G) complete,
(Am)The girls (C) all say as (Am) they pass me (E) by,
"(Am)Is that the (C)young man (G) they call (am) Rambleaway?"

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