No joy yet for Nicholas & Matthew, but I did find a Seymour Edgehill (Marriage 1765 Limerick) and a John Tempest Edghill (Marriage 1859 Belfast) on the IFF site.
Following up on JT has led me (v. poss wrongly)to Barbados where the Edghills seem firmly entrenched from c. 1660 on. Spelling for the family there varies: Edgwell, Edgell. Edgehill and Edghill (same goes for Ire & Eng). Moreover a Hippie Edgell (marriage 1807 Cork) can be traced back to Frome in Somerset Eng., as can (probably) an early Phillip Edgwell (Census: 1679 Barbados). So there does seem to be a Somerset/Ireland connection for all Edghill groups.
However I'd probably need to be in Ireland itself to unravel it properly (or as far as it'd go). There are only so many records available online.... though the fuller Irish 1911 census certainly helped as did the Irish Times archive from 1859.