Information on the numbers working part-time is published regularly in the civil service statistics:
http://www.statistics.gov.uk/StatBase/Product.asp?vlnk=2899&Pos=&ColRank=1&Rank=422
The Department offers a range of flexible work arrangements to employees including compressed hours, flexitime, home working, job sharing, partial retirement, part-time working and part-year working. Employees make applications to their line managers who take decisions based on business requirements.
The civil service operates a job share website which can be found at:
http://www.civilservice.gov.uk/jobs/jobshare/for-you/what-is-a-job-share.aspx
The Department's non-departmental public bodies are responsible for their own employee working arrangements and the information is not held centrally.