In about 1991, Dr. Lindsay Peer and Martin Chasedy (associated with the British Dyslexia Institute) came to Israel and trained a group of English teachers in the Hickey Method. The class included those teachers who went on to train hundreds of other Hickey tutors and teachers in Israel, and to become specialists in EFL for struggling learners.

Today there are courses in how to teach English by structured, multi-sensory, phonics-based methods in many teachers' colleges in Israel, including David Yellin College in Jerusalem, Gordon College in Haifa, Bar Ilan University and Kibbutz Seminar in Tel Aviv, Herzog College in Gush Etzion, Givat Washington College in Yavneh, and Beit Berl College in Raanana/Kfar Saba. 

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If you are a trained tutor in this approach, and want to be listed in a directory for parents and schools looking for qualified tutors or teachers, please fill out the form at the bottom of the tutor directory  (to view directory in Hebrew, change menu to Hebrew.)

The organization in the U.K. where Kathleen Hickey developed her program is now called Dyslexia Action (formerly Dyslexia Institute). From their web site:
"The largest dyslexia training provider in the UK; Our dyslexia training courses are accredited programmes that provide training for practitioners working in the field of dyslexia and specific learning difficulties (SpLD)."

An earlier version of the site stated that their training draws on the work of Orton and Gillingham in the USA; Kathleen Hickey, who developed her programme whilst she was their first Director of Studies; and the most recent research.

From the Wikipedia entry: 

Samuel Torrey Orton (1879–1948), a neuropsychiatrist and pathologist at Columbia University, studied children with language processing difficulties such as dyslexia. Together with educator and psychologist Anna Gillingham (1878–1963), he created techniques to teach reading that integrate kinesthetic (movement-based) and tactile (sensory-based) learning strategies with teaching of visual and auditory concepts.

In 1935, Gillingham, with her longtime collaborator Bessie Stillman, published the Gillingham–Stillman manual, Remedial Training for Children with Specific Disability in Reading, Spelling and Penmanship. This is now known as the Orton–Gillingham (O-G) method, "a multisensory phonics technique for remedial reading instruction."

IMSE is a commercial body that provides teacher training in the U.S. in the Orton-Gillingham approach. From their website, 

IMSE's Orton-Gillingham program educates teachers on how to explicity and effectively teach reading to beginning readers. Using multiple senses, children can better understand the rules of the English language. This is effective in the classroom because it allows educators to teach children in the way that each individual child learns best. 

From their website, IDA's mission is "To create a future for all individuals who struggle with dyslexia and other related reading differences so that they may have richer, more robust lives and access to the tools and resources they need." This organization advocates for the rights of dyslexic individuals, holds conferences and educates on issues related to dyslexia.