"UK Forces are specifically trained to act in the role of "Aid to the civil power". US Forces are expressly forbidden from doing this under US Law.

I'd have thought that would only apply within the United States, not in the situation of occupying forces in a foreign country. Occupying armies have very specific duties under international law, and maintaining order without "maximum casulaties" is one of these.

I think "the House Siege" did in fact end very badly indeed from the point of the occupiers and the regime they are trying to establish. I note that the UK envoy to Iraq has gone on record urgung that every effort should be made to capture Saddam rather than kill him.