http://www.nationalarchives.gov.uk/catalogue/ shows the index of Hyman's naturalisation information from 1927. A copy of this record should give you quite a lot of information about him.
It is also worth getting the marriage certificate, to see the names of their fathers and any witnesses, you might be able to find their family members in the UK also. freebmd.rootsweb.com shows other possible members of these families in London.
http://www.jeffreymaynard.com/LSyn31LR.htm - meanwhile this shows a J. Ostrofsky as an official at Old Castle Street Synagogue in 1931.
http://www.gazettes-online.co.uk/ - has a mention of Hyman at the time of his naturalisation - his occupation is 'Secretary of Registered Friendly and Approved Society'
The Times, Thursday, Oct 26, 1933; pg. 4; Issue 46585; col E
- Osterley, Hyman Joseph, passed the bar examination at Gray's Inn (Criminal Law and Procedure)
The Times, Tuesday, Nov 19, 1935; pg. 5; Issue 47225; col G
- list of those called to the bar, includes H. J. Osterley, LLB, University of London (Gray's Inn)
So it seems he changed his name a bit earlier than WWII - possibly when he entered law school.
ETA: Have you tried having a look at the Jewish Chronicle archives?