World Cup winners Bairstow, 34, and Moeen, 37, are the highest-profile casualties from those campaigns and could now have made their final England appearances.
Wicketkeeper-batter Bairstow was given a two-year England contract in October last year but was also dropped from the Test side earlier this summer while all-rounder Moeen retired from red-ball cricket for a second time after last summer’s Ashes series.
Bairstow has played 287 times for England across all formats and, like Moeen, was part of the side who won the World Cup in 2019.
Moeen, who 298 England caps and was Jos Buttler’s vice-captain at the past three World Cups, also won the T20 World Cup in Australia in 2022, a tournament Bairstow missed because of a serious leg injury.
Bowler Chris Jordan, another member of England’s T20 World Cup squad, has also been left out entirely while England say batter Joe Root, who has not played a T20 international since 2019, has been rested from the ODI squad.
Mark Wood and Ben Stokes are injured.
Buttler will return as captain, having missed The Hundred because of a calf injury.
Pace bowler Saqib Mahmood has been picked in the T20 squad. He has not played for England since sustaining a second stress fracture of his back last year.
Durham quick Brydon Carse has also been included in both squads, with his ban for betting offences set to end on 28 August.
With the first T20 against Australia coming on 11 September, a day after the conclusion of the ongoing Test series against Sri Lanka, Harry Brook, Gus Atkinson, Matthew Potts and Jamie Smith will only feature in the ODI matches.
Smith played two ODIs as part of a second-string England against Ireland last year but looks set for a more significant role following his impressive start to Test cricket.
All-rounder Liam Livingstone has only been included in the T20 squad despite being a regular in the 50-over side in recent years.
Mousley is more known as a powerful middle-order batter but impressed with his off-spin in The Hundred when he conceded just three runs and took three wickets when defending 10 runs from the final 10 balls for Birmingham Phoenix against Trent Rockets.
Barbados-born left-hander Bethell, who also played for the Phoenix, was part of the England squad who reached the Under-19 World Cup final in 2022.
Cox was picked in England’s squad for the first Test against Sri Lanka last week but did not play.
Having been released to play for Essex he hit a 92-ball hundred in the County Championship.