If you're looking for manga similar to Burn the Witch, you might like these titles.
Chasing a faint memory from childhood, Asuka Tsukasa travels to London—and falls headlong into fantasy, intrigue, and the piercing gaze of a beautiful beast girl!
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Both series are set in England with a secret society of some sort that deals with legends and/or monsters based on said legends. Both are heavily inspired by English Folklore and fairly short reads. Bestia (Makoto SANDA) is a completed story with a resolution and as of 2022 Burn the Witch has not gotten a continuation but it still could happen.
So in short if you're a fan of English Folklore and enjoy a low fantasy setting since both do occur on our Earth, You should give them a try!
Set in a world where innumerable dragons appeared and ruled the skies before humanity had the chance to be able to fly, Hitoe Kakujou, a first-rate witch flies through the skies freely on her broom.
British Empire under the reign of Queen Victoria in the 19th century. The stage is "Bray Rock Antique Store" like a graveyard, with a store in one corner of Imperial City London. Inside the store, there is a brooding young store owner "Bray Rock" and an innocent girl "Rila" who knows nothing. “Nancy,” a flower seller who visits the store every day to deliver flowers, touches the mystery of “Lilith,” the first witch of mankind, hidden behind the store one day!
Chise Hatori was a child nobody wanted. Told by her own mother that she should never have been born and passed from one neglectful guardian to the next, the young girl has grown up feeling lost, hopeless, and emotionally numb. At age fifteen she sells herself into slavery, desperate for a home where somebody - anybody - actually wants her to be there, and is purchased by a mysterious being with a skull for a head. He whisks Chise off to his home in England and introduces her to a world of talking animals, dragons, and faeries, declaring that she is to become his apprentice in magic... and also his bride!
In a castle atop a hill, in the south of France, lives a little witch named Lulu. Hidden away from the rest of the world and forced to wear a collier around her neck to control her powers, all Lulu wants to do is escape into the real world--and will stoop to anything in her mischievous attempts to leave! But her life slowly begins to change when her new teacher, a man named Camillo, arrives...
A young thief, Salt, and his partner-in-crime Pierre come across a strange-looking traveller with a penchant for sweets. The only thing of value Salt finds in the traveller’s bag is an odd compass, so he steals it – only for monsters to come after him a few hours later! Why are they after Salt? And what does the traveller want with him?? It’s a fantastic winter tale of magic!
A boy named Kouta Shibaki, who suddenly gets a bunch of magical tickets one day. Rurumo, a witch that was demoted to an apprentice witch, uses these tickets as training in the human world, and Kouta can use these tickets to grant wishes, which are part of Rurumo’s training. However, the catch is that each ticket that is used shortens Kouta’s lifespan, so will he help out Rurumo, even at the expense of his own life?