The dramatic reshuffle, which involves the restructure of the board, follows the sudden departure of managing director Chris Mottershead two weeks ago.
Peter Rothwell, chief executive for northern Europe, has stepped in as interim managing director to streamline the business and try to save millions of pounds in costs. Distribution director Miles Morgan will become sales and marketing director.
Edwards, who has been at TUI for four years, joins sales director Iain Fenton, who is also leaving. Head of PR Rachel O'Reilly will effectively replace Davies, who leaves after three years in her role.
Rothwell said: 'We have made huge progress over the past three years, but the pace of change is accelerating and I have decided to bring the UK businesses on to the same board to ensure we can focus on the challenges we face.'
TUI UK has struggled to adapt to fluctuating demand due to the Iraq war and fears of terrorism.