A survey by Ofsted of 20 teacher-training providers found that all had altered central parts of their courses since last September, when systematic phonics was added to the national curriculum.
The changes follow recommendations made in the Rose Review, in 2006, which said children should be taught to read primarily with systematic synthetic phonics by the age of five.
However, Ofsted also found that some training courses did not give teachers enough information on how to assess children's phonics skills, which could prevent them from intervening before children fall behind.
Some courses were also failing to highlight the links between early reading and writing, and not all providers were arranging suitable opportunities for trainees to observe high-quality phonics teaching.
Christine Gilbert, Her Majesty's Chief Inspector, said, 'It is very encouraging that, on the whole, teacher training providers are taking good account of the Rose Review's recommendations. However, more can be done to ensure that pupils' phonics skills are accurately assessed. Courses also need to do more to highlight the link between early reading and writing. And trainees need more opportunities to be able to observe high-quality lessons so they know how much children are capable of when they are taught phonics well.'