She was President of the Institute of Health Services Management in 1997–98 and is a past President of the International Hospital Federation. At the turn of the century, Morgan was chief executive of the North & East Devon Health Authority, based in Exeter where her husband taught at Exeter School. She was chief executive of the NHS Confederation from 2002 to 2008, chair of NHS Providers from 2014 to December 2019, and since January 2020 is the independent chair of the One Gloucestershire integrated care system.[2][3]
While working in healthcare, Morgan served on a number of national committees and working groups and was a member of the NHS Stakeholder Forum. She was one of the three members of the review team led by Sir Jeremy Beecham, set up in 2006 to advise the Welsh Assembly Government on the reform of public services in Wales.