Children should only be kept away from school for significant illness. If they have vomited or had diarrhoea, they should remain at home for 48 hours after the last episode.
Further guidance from Public Health England and the NHS on when to keep your child at home can be found below.

NHS - Is my child too ill for school?
Public Health - Infection Control in schools
 

Medical appointments
Every effort should be made to schedule routine medical appointments outside school hours or during school holidays. Where this is not possible and children are absent for all or part of the school day, you must show the office confirmation. This can be an email, letter or text message showing the date and time of the appointment.