I think Greg may have overstated his case this time around. He has pointed out the situational irony of a song/tune being used, which originated among people who would have had little time for Mrs. Thatcher.
Most Americans here will be aware of the way that Woody Guthrie's "This Land Is Your Land", originally a Marxist parody of "God Blessed America", has sometimes been adopted by those whom Guthrie opposed. The most ludicrous example was probably Bing Crosby's version, which omitted two of the most important verses.
You won't find many kind remarks about the late Mrs. Thatcher's policies from me either here or anywhere else. On the subject of her passing and funeral, I can live with the fact that there were those who admired her. I am not grieving, but those who loved the octogenarian widow will wish to bury their friend. I am not able to summon up any spite towards her now.
The policies are a different matter. On that issue I am with Greg all the way.