This is very interesting Teletabby! I swear sometimes the Liverpool accent sounds a bit Philadelphia to me. Perhaps there's a connection there?
Lots of people (Jewish & also I think, Irish too) immigrated to the US via Liverpool.
It's possibly, like Mrs R said. Personally, I think some Irish accents are quite similar to Liverpool, but it could be the influence of the ferries between ports wearing away at each dialect.
It's kind of fun looking at an area's history, and where and how it's dialects came from. This is easier for places such as North and South America, Australia & NZ and parts of Africa, as they were settled by Europeans...

With the UK it's a bit more difficult, but at the same time kind of simple, as you have the Celtic influences, as well as the Normans, Saxons and Romans. It's fun coming across proper Yorkshiremen (and women) who still speak a mix of Modern and Middle-English. ("Get thee home to thy mother!)