Reception teacher here struggling with the usual back to school insomnia. I wouldn't normally be posting at 3am but I simply couldn't read and run with this one.
Can I ask if you have a genuine reason for believing part-time until 5 is right for your child as an individual? (SEN, anxiety etc). Or is it more a pre-conceived idea you have that children start school too young in this country and therefore you wish to exercise your right to keep her part-time until compulsory school age, without considering her individual needs?
If it's the former, I would strongly stress your concern to the school and see if you can come up with a plan to best support her, working together to meet her individual needs. If it is the latter, and you're just wishing to follow this plan because it's what you believe in, rather than it genuinely being with your individual child's needs in mind, don't be surprised if the school aren't supportive I'm afraid.
The school won't be trying to change your mind based on funding, or because your wishes are inconvenient to them, as suggested by a couple of people. It will be because they know through experience how disruptive this will be for your child's education and social wellbeing longterm. I fully support a reduced timetable for those children who genuinely need it (complex SEN) but those whose needs mean they genuinely benefit from this are few and far between in my experience and even they will often find it very distressing having to leave their peers. Leaving at lunchtime will single your child out as being different. That would be my main concern as a teacher, that neither her nor her peers will understand why she leaves at lunch and the rest don't. This can also be very hard to adjust from midway through the year, if she's been use to a part-time timetable. Much better to start as you mean to go on in my experience. Full time schooling will be the norm once she's 5 (unless you home school) so she may as well bed into that routine now, alongside her peers, rather than struggle to adapt later.
Most children cope amazingly well with this and surprise their perhaps previously concerned parents, because they are genuinely ready. Reception is part of the EYFS. It's a vital bridge between pre-school and formal schooling. It's the year they practise being in school. They become part of the school community while still learning through play. They become accustomed to the rules and routines before they're expected to partake in formal lessons. Missing out on large parts of this transitional year can actually be hugely detrimental to children. As the post above rightly points out, you only have to look at the social and academic struggles of the current Year 3/4 cohort to see the effects of a disrupted Reception year. I really wouldn't advise doing that through choice.
The social impact of her missing lunchtime and afternoon sessions would be my main concern but there are academic concerns too. Reception is play-based learning, but the maths curriculum is heavily focused on mastery. It's not just about 'doing' maths, it's a about understanding maths. There's a reason Reception mainly focus on amounts to 5 until Christmas, and to 10 for the rest of the year. There is far more to maths than being able to count a set of objects or add or subtract some random numbers. That's pointless unless they have a true understanding of what those numerals they're working with represent. They will do so much work this year on subitising (seeing the amount without counting), spotting patterns and relationships between numbers and amounts, exploring number bonds, representing amounts in different ways, explaining their reasoning etc. School will teach her strategies which will stay with her and benefit her longterm to fully understand the number system once the numbers start to get bigger in Year 1 and beyond. If she misses that and just ends up with a superficial understanding of maths (through rote learned facts, as often can happen with children who do a lot of maths at home with parents through counting and 'sums'), she'll end up with big gaps in her knowledge face an uphill struggle to catch up.
She'll be learning all of that through carefully planned play-based activities, planned by Early Years experts. Isn't it better she experiences that and does it alongside her peers, having fun while she doesn't even realise she's learning, than going home early each day only to do maths activities with you anyway?
Her teachers are highly trained professionals who will have your daughter's best interests at heart. I'm not suggesting you don't, just that your concerns seem misplaced. If you are choosing to enter our school system and don't have clear reasons why you feel she as an individual needs to remain part time (indefinitely, until ready, rather than some arbitrary date where she'll have to go full time anyway) I would respect their experience on this one.
If you strongly don't agree with our education system to the point where you're prepared to disrupt your daughter's Reception year to make a point, rather than it being in her own individual interests, then I would strongly suggest you pull her out to home-school her full time as chopping and changing with part time schooling, singling her out as different to her peers, does not sound like it will be in her best interests.