I think the accent sounds very much like coming from just north of Exeter.
Dave, your Geordie friend is spot-on. Students of the UK accents can easily pinpoint towns - never mind counties. It's exactly the same in Scotland. A person born and bred in Glasgow can easily detect a Paisley 'Buddie' even though there's only 8 miles separation between the towns. Ayrshire people are completely different from Edinburgh folks and N. East natives have a dialect of their own. This is not at all strange and should not be to our American cousins either. Think about the difference between the speech of those from the north, south, east , centre or west of their vast country. Actually, the 'Standard', english as wot's talked by posh folks , is not really true. That way of speaking was an attempt to standardise the written and spoken language. I think it came about round the end of Shakespeare's life. Unfortunately Hollywood has a great deal to do with how other's perceive how Brits talk.
As for the origins of the way Americans speak - I suspect the Irish, Welsh and Scots had quite a bit of input there too. I always wondered how George Washington, Ben Franklin, John Paul(Jones)and some of the other famous American Fathers sounded like when they spoke. After all, the War of Independence started not long after the Jacobite rebellion of 1745 when huge numbers of prisoners and dispossessed family crossed the Atlantic for a better life.
Returning to Lightholler's BBC interview - it sounded to me he was reading it from a script. However he was reading it. Since he was actually there and we were not - why do so many doubt his recollection of the event. i.e he states categorically that the ship rose vertically and then plunged downward - no sign of a break-up. What would be his purpose in concealing that?