A Witch (魔女 Majou?) is a term simply used to describe certain magic users who have been active in England for a long time. They are part of the cause of why the anti-magical culture of England has developed unnaturally and thus are part of the reason of why Necessarius was created.  From their persecution it could be inferred that some of their magic practices defy the teachings of the church, even though it has been stated that their magic doesn't come from unnatural rituals such as cooking unbaptized babies nor something in those lines. 
They are formerly introduced as one of the organizations that the Knights of England try to hunt during Carissa's coup d'etat, in that opportunity they could quickly dispatch 100 members to repel their attackers, it should be noted that the "group" of the witches was simply referenced as Witches (魔女たち Majou-tachi?). 
After fighting off the knights, Kaori Kanzaki mentioned on how Necessarius contacted the witches, requesting their assistance in weakening the Curtana Original  . The witches for their part complied and after the joint operation Carissa lost half of the power that the Curtana gave her and the Knights of England pretty much lost their Telesma boost .
After damaging Curtana's power the Witches moved their mobile fortress outside England borders for the objective of launching a remote attack on the Buckingham palace . The target was at 500 kilometers and the actual estimated "effective" range of their Coven Compass was of approximately 330 km; yet regardless of that difference the attack was successful. The attack was meant to provide enough distraction, as to hamper Carissa's possibilities of doing an open counterattack on the rebel forces that would try to sneak into the palace . It should be noted that the Attack on Buckingham palace was actually authorized and made with the consent of the third princess Villian.
As an organization, it has been shown that the witches count with proper installations and proper magic practices to their group.
- Coven Compass (カヴン＝コンパス?) : A large mobile flying fortress that hovers for about 20 meters on top of the ocean, the mobile fortress is a giant disk made of stone with a diameter of 200 meters and thickness of 10 meters. The top of the disk had sharp lines running in each direction from the center which resemble an actual compass. The top of the fortress is the firing device for the large-scale flash spell that can be used to "fry" invaders, furthermore the fortress is constructed with several defensive measures to prevent anti-flying spells from knocking it down. 
- Magic Potion (魔女の薬 Majou no Kusuri?, lit. Witch's Potion) : A potion that can imbue flying abilities to objects.
- Smartvery (スマートヴェリー?) : While no leader position was properly stated within the witches, it should be noted that other witches requested advisable course of action from her.
- The actual full range of the "flash attack" from the Coven Compass was never directly stated, however Smartvery mentioned that 500 kms was a little bit more than 1.5 higher than the actual range of the weapon , meaning that 330 km is only a reasonably estimate born from that comment.
- ↑ Toaru Majutsu no Index Light Novel Volume 01 Chapter 02 Part 2
- ↑ 2.0 2.1 2.2 Toaru Majutsu no Index Light Novel Volume 17 Chapter 04 Part 1
- ↑ Toaru Majutsu no Index Light Novel Volume 18 Chapter 06 Part 3
- ↑ Toaru Majutsu no Index Light Novel Volume 18 Chapter 06 Part 9
- ↑ 5.0 5.1 Toaru Majutsu no Index Light Novel Volume 18 Chapter 07 Part 2
- ↑ Toaru Majutsu no Index Light Novel Volume 18 Chapter 07 Part 3