Bleeding Heart Yard in the London borough of Camden is where the Plornish family lives in Charles Dickens's "Little Dorrit" (1857). Its name is said to come from a Bleeding Heart pub situated there in the sixteenth century; the heart in question was the bleeding heart of the Virgin Mary. Bleeding Heart flowers have been called that since the seventeenth century. The modern sense of a "bleeding heart" as someone too sympathetic to the downtrodden is attested as early as 1951 and attributed without attestation to the anti-New Deal journalist Westbrook Pegler, who was kicked out of the John Birch Society in the 1960s for being too extreme even for them. (Andrew Shields, #111words, 17 September 2022)

An image of Bleeding Heart Yard from Walter Thornbury's Old and New London, 1873–8. (Wikipedia)

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Bleeding Heart Yard, in London and Charles Dickens's "Little Dorrit", and the history of "bleeding hearts"