The reshuffle, which also involves a restructured board, follows the sudden departure of managing director Chris Mottershead last week.
Peter Rothwell, chief executive for Northern Europe, has stepped in to streamline the business to reflect trends in the travel industry and attempt to save millions in costs.
Miles Morgan, previously distribution director, becomes sales and marketing director reporting directly to Rothwell, who has taken over as interim managing director. Edwards has left the company, having held the top marketing role for four years. Sales director Iain Fenton also leaves.
Davies, who has been communications director for three years, will effectively be replaced by head of public relations Rachel O'Reilly, now reporting to Morgan.
The board restructure also sees David Rowe, managing director of TUI's Specialist Holidays Group, leave the business and chief financial officer Will Waggott take the role of temporary managing director. UK finance director Fred Stratford also leaves.
Rothwell said: "We have made huge progress over the last three years in modernising our business, in streamlining functions and in delivering a consistent financial returns to shareholders, 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 together on the challenges we face."
Fewer people are now taking traditional package holidays, often preferring to source their own flights, hotels and car hire.
But TUI UK has also been hit by fluctuating demand due to war and terrorism fears. It has been accused of failing to adapt its capacity quickly enough to these flucuations.
Edwards took Thomson Holidays back on to TV with the first major branding campaign for three years earlier this summer.
A spokeswoman said all marketing activity was currently "under review".
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