George A. Matthew is probably George Alfred Matthew (1856-1905), who attended St John's College, Cambridge, before becoming a partner for 22 years in the firm of Ginn and Matthew in Cambridge. He was the President of the Cambridgeshire Law Society.
William Cole (1714-1782), Cambridge antiquary, studied at Eton, before attending Clare Hall and King's College, Cambridge. He was rector of Bletchley, Buckinghamshire, 1753-1767, and the non-resident vicar of Burnham, Buckinghamshire, 1774-1782. Cole bequeathed his manuscript collection, which consisted of material relating to Cambridge and its university, Huntingdonshire and Buckinghamshire, to the British Museum.
Sir Frederic Madden (1801-1873), antiquary, collated the manuscripts of Caedmon for Oxford University in 1825, and worked on the preparation of the British Museum's catalogue of printed books, 1826-1828. He became assistant-keeper of manuscripts at the museum in 1828, and was the head of department, 1837-1866.
From the guide to the Catalogue of William Cole Manuscripts in the British Museum, 1901, (Cambridge University Library, Department of Manuscripts and University Archives)