Mike, as you have her birth date the obvious thing to do is to find out from the Registry (address etc in my previous message) as to whether she has a birth cert under her surname Radcliffe, and if not, to try Kennaugh for the same date. If illegitimate she might have been registered under the mother's surname, even if both parents were given on the cert. The couple may or may not have married later.

However, in that births index entry I found, her surname is given as Radcliffe. Please give the Registry these details:
Year/ Surname/ Name/ District/ Vol/ Page No
1921/ Radcliffe/ Joan Kennaugh/ Rushen/ C/ 474

This fits the date you gave, because births were registered within a set period after the birth.

Sue