I didn't see this thread at the time, but following from the link in the thread on the earldom of Huntingdon- I looked into the ancestry of Charles Hastings (1794-1866), one of the founders of the British Medical Association, and came across references to a link with Warren Hastings (which I didn't find); based on my notes, there was no obvious connection between Warren Hastings and the Earls of Huntingdon, save mention that they were a 'senior line of the family from which the Earls of Huntingdon came also'. Several nineteenth century sources mention this in various forms, e.g. 'The Earls of Huntingdon, and the Marquis of Hastings, trace to a younger branch of the house of Daylesford' (the 1841 biography by Macaulay); 'during the suspension of the earldom of Huntingdon, the then proprietors of Daylesford claimed to represent the chief branch of the Hastings family.' (Chambers's Journal, 1884); 'The Earls of Huntingdon, once among the most powerful of the English aristocracy, took their rise from a younger branch of the house of Daylesford' (Memoirs of the Life of Warren Hastings, G. R. Gleig, 1884); 'In the dedicatory portion of the inscription on the Warren Hastings monument in Westminster Abbey, quoted in the preceding page, Mrs Hastings refers to her late husband as "descended from the elder branch of the ancient and noble family of Huntingdon."' (Life of Warren Hastings, First Governor-General of India, G. B. Malleson, 1894). Later, a 1916 edition of Macaulay's biography edited by Arthur D. Innes for the Cambridge University Press, had in a footnote: 'Hastings of Daylesford claimed to belong to an older branch of the Hastings family than the kinsmen who had been ennobled.' So it would appear that, even considerably later, no truth in this connection had been established.
Just in case it offers any leads for anyone else:
As Colin said, W. Hastings s. of Penystone Hastings (1704-1743), of Churchill, nr Chipping Norton, Oxfordshire, educ. Balliol Coll., Oxon., and Hester (-1732), dau. of - Warren. He 2nd s. of Penystone Hastings (1678-), of Daylesford, Glos. (sold 1715), educ. Balliol Coll., Oxon. (B.A. 1699), and Priscilla, dau. of William Gardiner, of Lower Guiting, Glos. P. Hastings (sr) 3rd s. of Penystone Hastings (1652-) and Elizabeth, dau. of Samuel Creswick[e], of Moreton-in-Marsh. This Penystone Hastings s. of John Hastings (1612-), of Daylesford, and of Yelford, Oxon., as well as four other manors lost supporting Charles I, and Elizabeth, dau. of Sir Thomas Penystone, of Cornwell. Of John I have a note: 'After the successive generations of Philip, Myles, Bartholomew, Roland, Thomas and John, comes John Hastings, the Cavalier, born 1612, who spent much of his substance in the cause of his King and at the close of the Civil War retired to live at St. Jean de Luz.' Unfortunately I didn't record the source! However, John's father, John (-1629) was of Daylesford, and m. [possibly 2ndly?] Susan, dau. of - Fettiplace.
For the record, Charles Hastings was s. of Rev. James Henry Hastings (1755-1856), rector of Martley, Worcs., and Elizabeth, dau. of John Paget, of Chipping Norton, banker; he was s. of James Hastings, of Hanover Square, London, a wine merchant; his father William, of Shipton-under-Wychwood, formerly of Chipping Norton.