Many immigrants went under their own steam or to join relatives already in the country.
During the Irish famine most of my great grandmother's family emigrated directly to the USA, but her father, the eldest, was married with children and couldn't afford fares for all his family and came to the UK instead, as his children grew up many of them saved the money to emigrate to join the family in the US. My grandmother gathered the money for her fare, but then fell in love in the UK so married and stayed here.
We traced family through the Ancestry passenger list sources and Census returns in the USA.
Last weekend, in Rutland, the first statue in Britain of the late Elizabeth II was unveiled.