Major ports were London (+ along Thames) , big naval ports at Portsmouth + Plymouth (but not sure re civilian), Bristol, Liverpool (possibly still Chester at an early period but Liverpool was on a very fast growth from around 1700 onwards and for manx emigration would possibly be my choice), Lancaster (quite big in Slaving) Whitehaven (the packet from IoM went here until early 19th C) and further north those on the Clyde;
You also have the Irish ports
The US act requiring manifests came in 1819 though I think at some ports earlier lists survive