You asked

I notice that the General Household Survey (GHS) - which I believe ran until 2007/08 - collected information on the gap between the 'expected' number of children a woman sought to bear, and the 'actual' number of children that she eventually did.

I understand that the GHS has now been merged into the Integrated Household Survey, but am unable to find this information on the gap between 'expected' and 'actual' children.

If you could point me towards the new incarnation of this survey data that would be much appreciated.

We said

Between 2008 and 2011, the General Lifestyle Survey held these questions then the Opinions and Lifestyle Survey took the questions over from 2012 to 2014, and it was then ceased. This data is available on the UK Data Archive: http://www.data-archive.ac.uk/about