The Mixed Commission on British and American Claims were asked by British subjects to determine whether "the 'city was wantonly fired by the army of General Sherman'9 with his 'consent and connivance' resulting in the destruction of their property." [See: Link]
The Commission, faced with conflicting testimony, came to the conclusion that the fire " 'was not to be described to either the intention or default of either the Federal or confederate [sic] officers,'12 a kind of nondecision which seemed to say that the results of war could not be changed." [same source as above] Of course, the US representative on this three-person Commission was a Republican judge from Indiana. The Commission considered a huge number of claims, not just Columbia.
Let's see. Cities and towns were burned along the path of Sherman's army before it got to Columbia and along its path after the army left Columbia. Columbia was just part of a pattern. His troops figured out what they could get away with as far as looting and burning. Sherman appears to have been looking the other way when all of this occurred, although he does say in his wartime correspondence that he burned Rome, Georgia, and intended to burn Atlanta in a few days. I posted some of the Union correspondence and newspaper reports before [see Link].
As far as who burned Columbia is concerned, Simms' first hand reports are very clear that the Federal soldiers did it. If you think he is perhaps a biased reporter of what happened, consider the report of Union Captain George Whitfield Pepper in his 1866 book, Personal Recollections of Sherman's Campaigns: In Georgia and the Carolinas. Pepper reported that that he saw crowds of soldiers returning from Columbia "waving gold watches, handfuls of gold, jewelry, and rebel shinplasters [rb: paper money] in the air, and boasting of having burned the town." Pepper also confirmed Simms observation that Federal soldiers kept cutting the fire hoses of the Columbia fire fighters trying to put out the fires: "The fire companies brought out their engines and our men cut the hose to pieces."
Here are some additional links for you. I have hard copies of Lucas' book (the first link above), the Aiken version of Simms' book [here is a link to an 1865 version of Simms' book], and Pepper's book [Link].
In the matter of "Who burned Columbia?", there was ample evidence presented that looting and arson was committed by retreating confederates (specifically Texas Volunteers under the command Col. Wheeler) acting on the orders of General Wade Hampton before the Union army ever entered the city.
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