I need the percentage of detached homes out of all homes roughly during 1900-1920. Also, the percentage of private homeownership in the same historic period. Data for Birmingham would be especially helpful.
You might want to check with some of the folks at the Harvard Joint Center for Housing Studies. My former boss at NAHB, Kent Colton, used to work there and wrote a book called "Housing Policy in the United States" in 2005. There were some reference to cross-national home ownership rates, but more of a static and not a historic nature. One guy who still works there is a guy named Alexander von Hoffman who I feel is very knowledgeable and might be able to help.
You might also want to check out the Economic History Association. I do not know anyone specifically there that would know that, but they are a helpful group that might have a listserv where you can post the question. (https://eh.net/eha/)
University of Portsmouth has a really useful, publicly available resource called The Great Britain Historical Database. It covers all censuses from 1851-1961 and is easily searchable by specific location. It covers various aspects of housing, including a number of subsets split under tenure type. However, I'm doubtful that tenure type was collected in the majority of 19th Century censuses.
Entry is through http://www.visionofbritain.org.uk/gbhdb/, you can download maps, spreadsheets and it will draw graphs etc. A wonderful free resource!!!