Firstly, the 1911 census is the last publicly available census under the 100 year rule for release of government records in the UK. The only later census type records is the 1939 register compiled for issuing identity cards during WW2. May be worth while checking there as I have found info that fills in gaps from earlier in the 20th century
You are correct about Russia often referring to Russian Poland, or anywhere in the Russian empire.
There were no passenger manifests for journeys between England and Continental Europe at that time - I've tried that route - in fact many immigrants did not come on passenger steamers but on fishing or cargo ships.
There was an optional naturalisation process - it was not mandatory - you can search the Public Records Office Discovery database by inputting in the relative's name. If an index record is found, you can request a quote for copying the contents of the file concerned, and then order the copy. However due to Covid, the service may not be available at present. If you can get the file, you may find useful information on where exactly (town) they came from and on parents, children, dates of birth, etc
Also if any children were born in the UK after arrival, their birth certificates may give info on mother's first name, maiden name, etc if you don't know that. Be prepared for errors due to transcription errors, etc, Use gro.gov.uk to order the actual certificates (sometimes they can send a pdf). Use either ancestry or freebmd.org.uk to get the registry entry details (registration district, year, quarter and volume/page number) that you will need to order the certificate.
Finally try jri-poland for searching for information that predates emigration to England