The North West of England was subject to a lot of immigration from Ireland, especially after the 1840s when many poor, desperate Irish people flooded into Lancashire to escape the famine and look for work in the cotton mills. When I was doing some work for my history degree dissertation I found out that about 10% -15% of the population of Manchester was Irish-Born (not including those born in England but of Irish descent) and this figure was even higher for Liverpool, at 18%-20% (again, not including their children born in England).
I suspect the similarity in accents and pronunciation in the Northwest of England and the Appalachians etc stems from a common Irish cultural influence, rather than emigration from the North West of England into the Appalachians...
Sounds like a good assessment. There has been a lot more movement around, in, from, and through the British Isles than many realize. During the 19th century, many Scots went to Yorkshire and Lancashire in search of work. I don't know that they had much influence on the Yorkshire dialects, which are varied and largely incomprehensible, but they developed the Yorkshire Terrier from Scottish terrier breeds they brought with them.