Thank you for your replies. James and Charlie do eat a diet that is extremely restricted to the said foods. They have suffered bowel problems at times, e.g. going through phases of going 3-4 times a day each for several weeks and always have runny nappies. (Apologies for the detail!) James also suffers quite badly with eczema.
Whatever our paediatricians view is, I think that we will end up trying them on the diet because I just feel otherwise I will always be wondering if it might benefit them.
Sophie x