Listed first are some academic studies.

London, Docklands, England
Dr Morag Stuart carried out a study in London’s Docklands where almost all the children speak a dialect of Bengali called Sylheti. (The families were recent immigrants from Bangladesh). While the experimental group was taught Jolly Phonics. the control group was taught with big storybooks, a popular method based on word memorization. The results are summarised at the base of the page numbered 602. The results show a large average difference from the teaching method used. They also show a major difference in underachievement. And finally, they show that this kind of phonics teaching is highly suitable for children with English as a second language.
Getting ready for Reading: Early phoneme awareness and Phonics Teaching Improves Reading and spelling in inner-city Second Language Learners – by Morag Stuart

Clackmannanshire, Scotland (after 7 years)
A later study in Clackmannanshire, after 7 years, answered the question of whether the children retained their gain in literacy. This paper summarises the results on page 8, paragraph 3. As shown, their literacy skills had improved further.
Clackmannanshire after 7 years

Yorkshire, England
Professor Maggie Snowling, Professor Charles Hulme, and others studied young children with poor oral language before starting school. They compare two different interventions, one with extra phonological training (using Jolly Phonics) and one with extra oral language training.
Yorkshire results

Montreal, Canada
Dr Yvette Hus carried out an early reading project on at-risk students who have English as a second language, to see whether Jolly Phonics improved their ability to become literate in the language, which indeed it did.
Montreal report

Hyderabad, India 
Dr Pauline Dixon researched the use of Jolly Phonics in low-cost private schools in Hyderabad.
Hyderabad study

Japan
Professor Yusawa of Hiroshima University wrote this award-winning paper (in Japanese) about Jolly Phonics, for the Japanese Association of Educational Psychology.
Japan report

Bristol, England
An early study into Jolly Phonics was carried out by Dr Marlynne Grant at St Michael’s School in Stoke Gifford, Bristol. The link below is to the results published at the time. The Second Cohort is significant (where the teaching was for a full year). It showed a large average gain in reading age and important other findings. Not only did the boys do as well as the girls, but there was no difference in whether children had free school meals (a measure of social class).
Bristol results
There is also a Jolly Phonics case study on this school from the same time:
Bristol Case Study
In addition to these studies, there are some Jolly Phonics case studies on individual schools, written by those at the school and with their evaluation of the results. The full list is published here, but the ones with quantitative data available on those from Elgin IA, Seoul Korea, Yorkshire, Sydney, and Bristol

France
“Des écoles anglaises au top: La révolution de la lecture dans les écoles publiques défavorisées.” Les Débats de l’éducation, Numero 2, Octobre 2012.

Italy
Daniela Caserta examines the implementation of Jolly Phonics in two schools in Milan, Italy, where the children are learning English as a second language: one private international school and one Italian state school. Writing in Italian, she makes recommendations concerning the training of Italian teachers to deliver the program. She proposes that an early introduction of English through Jolly Phonics in Kindergarten would yield the best results.
Un Approccio alla Lingua Inglese con il Metodo Systematic Synthetic Phonics (104 pp)

Indonesia
Dr Lisnawati Ruhaena researched the use of Jolly Phonics for the initial teaching of literacy in both Indonesian and English. The abstract of this report is in English, while the text is in Indonesian.
Indonesian report

Australia: Remedial use of Jolly Phonics Extra
Australian remedial report

Joliet, Illinois, USA
Dr Lori Motsch researched using the Jolly Phonics Letter Sounds app on the iPad as a remedial intervention.
To read Dr Motsch’s report, click here.