The AIRLINE is Thomsonlfy, the company CHARTERING the aircraft is Fred Olsen or P&O.
If someone is prepared to contract with Thomsonfly (the airline) and pay them a seat rate which Thomsonfly (the airline) find acceptable then they will fly from pretty much anywhere in the UK to pretty much anywhere overseas. If you offer them £100,000 and ask them to fly you and your mates down to Spain for the weekend, I'm sure they will oblige.
This however has almost no bearing on whether TUI (the tour operator) will commit to offering package holidays out of the same UK airport, be it with thomsonfly (the airline) or any other airline for that matter.
The point is, by definition, there are two parties involved in a charter flight and just because you see a Thomsonfly aircraft doesn't mean it is being chartered by TUI.
Hope that is clear