Similarly did she have a contract of employment and wage slip. This sort of casual approach to employment law is common for young people working in small businesses, where they are undoubtedly earning well below the tax threshold. A similar lax attitude to health and safety requirements is also rife. To be honest unless you feel they treated your daughter appallingly and you want to push back I wouldn’t make a thing of it. I doubt it will be on HMRC priority list to crack down hard on this. Better to choose a bigger employer or to confirm arrangements at the start for the next job.