Try the National Archives. They record all naturalisations and are a great, if expensive, resource. If you can find the right record, not so easy when there maybe several people with the same name, you can purchase a copy of the file which may give a few interesting nuggets of information.  From a great aunt’s file I found out my Olesinksa great grandparents owned a restaurant in Poland pre War; a fact unknown to any living member of the family.

you can also try the BMD registers if you have some idea of the relevant dates but the transcription errors can make that difficult sometimes. 
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Genene Collins
Bushey, Hertfordshire, UK
genene@...
Poland, Baum, Berman, Heuberger, Kapelner, Kohs, Szylit, Olesinkska

Hi Rick

Ancestry has passenger lists for incoming to UK as well as the Hamburg passenger lists. I think the Hamburg lists definitely should be searched. You do need a Worldwide subscription on Ancestry to do the search. Also check the England outgoing passenger lists as they or members of the family may have travelled from England at a later date.  

Arlene Beare UK
Trzmil Kohn  and Dembinski Zychlin Poland.
Samuels UK  Dorfman Birzai Lithuania
Bloom and Sher Pandelys Lithuania  and Riga Latvia

1874 is too early for records of migration to Britain - there are very few records available.  My family all arrived between 1865 and 1875 either via Hull on the East Coast of England or Leith in Scotland, but there are no official records to show this.

Naturalizations are the best way to find approximate date of arrival in Britain, as applicants had to get sponsors to say they knew them from such and such a  date, and they had to give their previous addresses in the UK and the dates that applied .  However, not all people naturalized as it was not compulsory, and it was expensive, and some people re-migrated again to North America, South Africa or Australasia. 

Dr Nick Evans of Hull University is the expert on migration from the Baltic/North Sea areas to and from Hull (and UK generally) and we hope to have him at IAGJS in London in 2023. 

Jill Whitehead, Surrey, UK