In fact, I think 'Come a-dancing the Iron Lady to" is a slightly unusual word-order inversion that turns up now and then in folk songs. I think 'come' is a past tense here (have heard this several times in Carthy folk songs, can't think of examples offhand). The sense is 'came dancing to the Iron Lady' as in 'dancing to her tune'; he's saying 'lay the blame at Thatcher's door', *she* set the whole thing in motion. This follows the sense of the verse slightly better IMO: it's a final summation and condemnation of the City and Thatcher.

May be wrong, as have no connection with either Carthy or the contents of Carthy's head, but this makes sense to me.