The Quality Assurance Datapack, included in the initial release of 2011 Census data on 16th July 2012, provided overall response rates for local authorities in England & Wales. That data is now supplemented by a more detailed breakdown of response rates by characteristics including age, gender, ethnic group, marital status, country of birth and tenure.
The data can be downloaded, along with methodological papers and a report on response rates, from the ONS website.
SASPAC 