https://www.ucl.ac.uk/child-health/short-courses-events/centre-applied-statistics-courses
UCL run different courses on statistics - no prior statistical knowledge is assumed for the introductory course (Introduction to Research Methods and Statistics), or their summer schools, but all other courses assume that the basics are understood. Courses usually take place weekdays between 10.00am and 4.30pm. Selected evening courses that run between 5.30pm and 8.15pm are often available.
You can also undertake an MSc at UCL. They offer five pathways in Paediatrics and Child Health, each of which can be taken as an MSc, PG Dip or PG Cert. https://www.ucl.ac.uk/child-health/study/postgraduate-taught-programmes/paediatrics-and-child-health
The Advanced Paediatrics MSc course at King’s College London is a multidisciplinary master’s degree designed for doctors, nurses, pharmacists and other allied health professionals. This advanced study course concentrates on expanding your research and evidence-based evaluation skills in clinical practice and leadership, as well as enhancing your career opportunities in research and academia.
https://www.kcl.ac.uk/study/postgraduate/taught-courses/advanced-paediatrics-msc
Imperial run an Applied Paediatrics Msc. The modules on offer including cover the science and evidence in paediatric practice.