it might be worth you checking google flights, the TUI aircraft types are now showing, but of course all subject to change!
Birmingham is currently showing 2 787s based for summer 2022, 1 presumably a 789 will do long haul every day, the other a 788, is scheduled to operate short haul flights Monday-Saturday, and a long haul flight on Sunday. Pretty certain Gatwick and Manchester will also have short haul flying on the dreamliners.