Sir Thomas More was the English councillor who stood against Henry VIII's decision to divorce and remarry. He was subsequently beheaded for his stand and was later canonised by the Catholic Church. There were other great Britons by the name of Moore as well (double o) which the poem may be referring to.
Peckham is a district of London with an ethnically diverse community. If you look on the Wikipedia page, you may find some clue about why it was referenced. ;)
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