The only scheduled flights, direct to Innsbruck, are from Gatwick. They are operated by GB Airways and Austrian Airlines. The timetable is here:
http://www.innsbruck-airport.com/index.html/_a/346693/_s a/346705/_z/350610/_lang/en
As has been stated in response to your other post, there's a charter flight from Exeter on Saturdays. The operator is Austrian Arrows.
There's also a Saturday Charter flight from Bournemouth. The operator is Lauda Air.
Other charter flights from the southern half of England are as follows:
Bristol (Saturdays) - Lauda Air
Gatwick (Saturdays) - Thomas Cook
Gatwick (Saturdays) - Monarch
Gatwick (Sundays) - Astraeus
Gatwick (Sundays) - Monarch
Gatwick (Saturdays) - First Choice
Stansted (Saturdays) - First Choice
Stansted (Sundays) - Austrian Arrows
Luton (Saturdays) - Austrian Arrows
Gatwick (Sundays) - Excel
Chris