You asked

I am looking to gain some statistics on unwed mixed ethnicity couples having children. For example, White man and Indian woman having a baby and not being married.

We said

Thank you for your request. The requested statistics are not held in the format requested.

The Census Commissioned Tables team have found the following relating to the topic: CT0365 - Ethnic group of father (where present) by age of mother by ethnic group of mother by ethnic group of infant (aged 0) - London region only

http://www.ons.gov.uk/ons/about-ons/business-transparency/freedom-of-information/what-can-i-request/published-ad-hoc-data/census/ethnicity/ct0365-2011-census.xls

Link to page relating to short stories on the topic containing 2001 and 2011 data:

https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/marriagecohabitationandcivilpartnerships/datasets/2011censusanalysiswhatdoesthe2011censustellusaboutinterethnicrelationships

DC1201 - Household composition by ethnic group of HRP - Population: Household:

https://www.nomisweb.co.uk/census/2011/dc1203ew

Please contact our Population Estimates team if you would like to discuss further - pop.info@ons.gov.uk