The Dolphin family are treated in Ruvigny's Plantagenet Roll of the Blood Royal, Essex Volume, but I don't have it and can't see the full pedigree on Google books. BFI gives 'Dolphin of Turoe', but there doesn't appear to be a link.
E. H. Dolphin was son of Rev. John Maximilian Dolphin (1837-), educ. Oriel Coll., Oxon. (B.A. 1860), vicar, formerly perpetual curate, of Coddington, Notts., and his wife Rose, dau. of Per Alumni Oxonienses, his father was Rev. John Dolphin, of Antingham, Norfolk. This elder Rev. John Dolphin, per Walford's County Families (1864 and 1871), was b. 1804, s. of another Rev. John Dolphin (-1830), of Copford, Essex, and Martha, dau. of Lock Rollinson, of Chadlington, Oxon. He was educ. Eton and Trinity Coll., Cantab. (B.A. 1828) and m. 1833, Mary, dau. of 'the late Admiral Western, of Tattingston, Suffolk'. In addition to being rector of Antingham, he was vicar of Thorpemarket, and a magistrate for Norfolk [some details, including his death in 1889, here:
https://en.wikipedia.org/wiki/John_Dolphin_(cricketer)].
The origin of the 'Hippisley' name in the Dolphin family is indicated by the appearance- in at least several pre-1900 editions of BLG, the pedigree of Hippisley of Lamborne (descended from which family were the Hippisley-Coxes) [per BFI this is later 'Hippisley of Ston Easton'; it also gives 'Hippisley Coxe (see Buller; and Hippisley-Cox)'] - of a John Hippisley, of Stone (sic) Easton, Somerset, who m. 2ndly, 1843, 'Georgiana, second dau. of the late Rev. John Dolphin, rector of Wakes Colne, and Pebmarsh, Co. Essex.' Given the dates, this Rev. John Dolphin is presumably he of Copford, who d. 1830 (see above) [a check of BMD records shows Georgiana, b. 1808 to John Dolphin and Martha, corroborating this]. Per his death notice in 'The Gentleman's Magazine', vol. 149 (1831): 'At Stanway, Essex, the Rev. John Dolphin, Rector of Pebmarsh and Colne Wake, and Prebendary of York. He was of Christchurch, Oxf. M.A. 1799; was collated to the prebend of Riccall in the cathedral of York in 1818 by Archbishop Vernon, presented to Pebmarsh in 1823 by the Earl of Verulam, and to Colne Wake by the same patron'. A marriage record shows that he married Martha Rollinson in 1803 at Cheltenham; no parents' names are given. Alumni Oxonienses, however, provides: 'Dolphin, John, s. John, of Shenstone, co. Stafford, arm. CHRIST CHURCH, matric. 3 June, 1791, aged 16; B.A. 1795, M.A. 1799, preb. of York 1813, rector of Pebmarsh and Colne Wake, Essex, 1823, until his death 1831.' A 1774 birth record for John Dolphin at Shenstone corroborates his father as John, and gives mother as 'Margret'. Annoying not to be able to see the Ruvigny volume which might go further back!