My ancestry, well half of it, can be traced back to Devon.
At one point I had a discussion with one of my family contacts about why an ancestor, Samuel Halls, would be assigned an Irish ancestry in census and death records, when we knew he was from England. That lead us to speculate about what kind of an accent that our ancestors would have had. I guessed that Samuel and his brothers had an accent that sounded Irish to the untutored ear of the late 1800's and early 1900's.
Since then I have found sound recordings of Devon residents born in the late 1800's, and books describing the accent written in the 1800's. The recordings were made in the late 1950's and early 1960's, so I suspect that what we are hearing is echoes of the old Devon accents, flattened out after most of a lifetime of exposure to radio and later tv. I have listened to the recordings, and the accents change every once in a while when the speaker talks. At times the accent seems to become stronger, and then it fades to something closer, but not identical to, a modern "english" accent. There are, to me, echoes of an Irish lilt, but they are not strong. Perhaps to an outsider, coming amongst native Devonians (Devonites?) at the time (1800's) that accent may have sounded Irish. And of course, Samuel Halls had spent almost 65 years in Canada before he died, so who knows how his accent would have sounded when he died in 1906, compared to when he came over in the 1842?
Historically, from what I understand of the history of the area, it would be possible to have some sort of Celtic/Gaelic language influence on the English dialect of Devon. Geographically Devon is bounded on the west by Cornwall, on the northwest and west across the water are Wales and Ireland, to the south is Brittany. Only to the east are there english speaking areas, Somerset and Dorset, all the other areas mentioned speak (or spoke) a language from the Gaelic group of languages.
If you are interested, here are the books on Devon accents:
The Peasant Speech of Devon, by Sarah Hewett published in 1892. You can download/read it at http://www.archive.org/details/peasantspeechofd00hewe.
Jim and Nell: A Dramatic Poem in the Dialect of North Devon, published 1867. It can be download/read it at http://www.archive.org/details/jimnelldramaticp00lond.
The last is A Dialogue in the Devonshire Dialect, published in 1837, but compiled sometime in the mid 1700's! It can be read/downloaded at http://www.archive.org/details/dialogueindevons00palmrich.
The sound files can be found at the Survey of English Dialects which opens up the page that contains Devon. Check for the birthdate of the speaker once you open a link. Alternately you can start at the Archival Sounds Homepage of the British Library.