Kevin Pietersen, struggling with a calf strain, has been retained, but James Taylor has been added to the squad as cover for the Test, which begins on August 1.
Spinner Monty Panesar, who bowled tidily against Australia in the tourists' warm-up match at Sussex, has been added, as has Surrey paceman Chris Tremlett, who has not represented his country since January 2012.
Steven Finn has been dropped from the squad altogether, as has fellow seamer Graeme Onions.
Despite the change of personnel, if Pietersen has recovered from the calf problem which prevented him fielding at the end of the second Test at Lord's, England could yet go into the third Test unchanged.
"The players worked hard at Trent Bridge and Lord's to get into a very good position in this Ashes series," said national selector Geoff Miller, "but will be fully aware that there is still a great deal of cricket left in the series.
"The players have had some time this week to recover following back-to-back Tests and an opportunity to work on aspects of their game and they will arrive in Manchester determined to build on their performances over the last two Tests.
"Kevin Pietersen is continuing his recovery from a calf strain and he will be assessed by the medical team closer to the start of the Test and we have therefore included an extra batsman in James Taylor who has been in good form for Nottinghamshire this season.
"Chris Tremlett has worked hard to regain fitness and form following a couple of injuries and his performances for Surrey this season have been very encouraging.
"Including an additional spinner in Monty Panesar who has plenty of international experience provides Alastair Cook and Andy Flower with a number of options."
Full Ashes squad for the third Test at Old Trafford: Alastair Cook (c), James Anderson, Jonny Bairstow, Ian Bell, Tim Bresnan, Sutart Broad, Monty Panesar, Kevin Pietersen, Matt Prior (w), Joe Root, Graeme Swann, James Taylor, Chris Tremlett, Jonathan Trott