Parents can be fined for taking children on holiday during term time. I know of some parents who choose to pay the fine, because even with the cost of the fine, it would still make a holiday cheaper.
This would be classed as unauthorised but if parents are open and honest with the school about it then the school is able to record an explanation for the absence.
You can apply to the Head to authorise the absence (and so avoid the fine) but it's at the Head's discretion. I'm surprised to read of people's experiences of absences not being authorised on account of things like funerals - in my experience of working in schools, such requests have always been given. But then I can't speak for every school.
In terms of other consequences of unauthorised absences, it really depends on the context and individual circumstances.
So, in the case of the OP, where it clearly is a genuine medical appointment, the absence might be initially marked as unauthorised as the school were initially unaware and planned absences should be authorised by the Head. The receptionist legally cannot authorise it, so if a parent or carer turns up to collect they legally have to mark it as unauthorised. I would expect that it would then be changed to authorised once the circumstances are confirmed.
In cases where there are persistent unexplained absences, the school has a legal obligation to follow this up. In theory, there should be no unauthorised absences on the registers by the end of the day. Or if there are, the school has been in contact with parents/ carers and it is clear that the child is safe and not missing.
It may be that a child is school refusing and the reasons for this are many and varied, and very challenging for parents who are doing there very best to get them into school. If anyone is in this situation, please do contact the pastoral/ welfare teams at the school so that they can support you. The cases of school refusal have increased significantly since the pandemic. No parent should be made to feel like they are at fault. My advice is to keep an open line of communication.
As you can imagine, keeping on top of attendance in schools is quite a mammoth task for the admin teams in schools. The colleagues I work with do an amazing job - there are 1500 students at the school. If I haven't saved my class register within 10 mins of the lesson, I will get a general reminder to do it 🤣.
I know it might feel frustrating at times for parents but I would say that if your child's school seems quite strict about absences, then it means they have really good safeguarding systems in place.
I imagine that the receptionist in OP may well have had a busy afternoon dealing with a number of parents arriving unannounced asking for their child to be taken out of class early - it's quite common on the last day of a half term. This puts pressure on staff to alert relevant teachers and interrupt lessons. I imagine she was probably having a bad afternoon.
C