I suggest you look at records held by 1) The UK National Archives online for migration 2) The University of Hull 3) Hull Maritime Museum and also Grimsby Maritime Museum, both ports on the River Humber 4) Hamburg port records- all available online. Also 5) Shipping line records especially the Wilson Shipping Line of Hull. NB there are few if any passenger manifests for any migration at this time as either they were not kept or they were destroyed.
My ancestors came over to Northern England and Scotland between 1865 and 1875, they came by sailing boat to Hull or Leith, the port for Edinburgh. Others went to the Port of London, or to other ports in NE England e.g. Newcastle on Tyne.The new deep water port of Grimsby opened in the early to mid 1890's from memory, to take steamships.
Many sailed from Hamburg in the 1890's, after train trips from elsewhere in Estern Europe. My ancestors probably sailed from either Libau in Latvia or from Konigsberg - they lived on the border with Konigsberg, and there was a lot of human smuggling that occured across that border for those who had been called up by the Tsar to his army.
Jill Whitehead, Surrey, UK