Jesus, and didst Thou condescend appeared in Charles Bradley's Psalms and Hymns selected and arranged for Public Worship published in 1828 by Hamilton, Adams and Co. in London. He is not the author. The hymn is taken from J. Curtis's "Union Collection" of 1887 where it is signed "Am---a" probably Amelia -- Our Hymns: their authors and origins by Josiah Miller, 1864
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Jesus, and didst Thou condescend? [The Miracles of Christ.] This hymn appeared in the Bristol Baptist Collection of Ash & Evans, 1769, No. 224, in 5 stanzas of 4 lines, headed, “Imploring Mercy," and signed, "Am—a." In The Union Collection of Hymns and Sacred Odes, &c, by J. Curtis, of Bristol, 1827, No. 56, it was repeated in 4 stanzas, and signed as in Ash & Evans. In this form it has passed into several collections, including the New Congregational Hymn Book, 1859; Laudes Domini, N. Y., 1884; and as "And didst Thou, Jesus, condescend?" in the American Baptist Hymn [and Tune] Book, 1871.
As to the authorship, D. Sedgwick has given in his manuscript, "Amelia Curtis, 1827,"and on a fly-leaf of a copy of the 1827 edition of Ash and Evans, "Amelia Wakeford." The New Congregational Hymn Book gives "Bradley," and Laudes Domini "Mrs. Amelia Wakeford." Possibly this last may be right, but we have no positive evidence either way (Sedgwick's contradiction of himself renders his evidence valueless), and must leave it as in Ash & Evans, " Am—a."
--John Julian, Dictionary of Hymnology (1907)