The occurrence of autism in eight-year-olds reached a plateau in the early 2000s and remained steady throughout 2010, they found.
Writing in the online journal BMJ Open, the experts said the cause of the surge seen in the 1990s "remains in large part a mystery".
One explanation is changes to the way autism was diagnosed, which captured more cases, but this is unlikely to explain the five-fold increase seen.
Experts including from the University College London Institute of Child Health, analysed data from the General Practice Research Database, which contains around three million anonymised patient records from UK surgerie.
The typical prevalence of autistic spectrum disorders each year was estimated at 3.8 per 1000 boys and 0.8 per 1000 girls. The annual number of new cases was estimated at 1.2 per 1000 boys (1,190 in total) and 0.2 per 1000 girls (217 in total). Girls were about 75% less likely to be diagnosed than boys.