UmmH- Sudbourne is a fantastic school with a really good parent community. My DC don't go there, but we are in a nearby. My DC all started at another nearby 'outstanding school'. Sudbourne is by far better. I know loads of kids and families there and many go on to top schools both state and private.
There is always a debate re- state vs private and it is a personal choice and often a political one depending on who you are. No need having that debate here.
My DC all went to our local state primary. It was and is by no means perfect in nearly every category. It was good in the early years and being able to walk to school and be part of the local community was a real plus. There were also some very good teachers. Some really bad ones as well.
The later years were and are a mess. My DD went on to a top selective state school. Very hard to get into and she also got into 2 top privates. I did have to prepare her myself. Wh Smith has all the books. The school did nothing and as she was bright she was pretty much left on her own for the last 2 years of primary except for one year 5 teacher who took a shine to her and sadly left the school after one year. I don't think Sudbourne is like that from what I've heard from families there. So that is a real plus. It just depends on the leadership of the school and what they think is important. My school does very well at raising the achievement of the lowest academic group. They don't do much for the middle and the top kids. Only enough to tick a box. It is pretty pathetic.
My middle DS is very bright and was bullied terribly for several years at this school until he was so seriously beaten up during playtime I had to remove him. He is now at a private school. I can say it is a different story at the private school regarding kids attitudes to learning in the later years, kindness, opportunity and the arts. I won't need to do much work preparing him for exams next year because it is part of the curriculum at the private school. He wasn't behind when he got there. He's been put in the top sets, so education wise there wasn't much difference except that he has other kids like him rather that sticking out as the smart one. That has raised his confidence. It's also a more peaceful atmosphere. It's cushioned and soft and not really London, but that was what he needed after his time at the other school. Happiness does make a difference.
There are benefits to being in a London State school and kids learn valuable skills, but depending on your child the pros may not be as positive and the negative cons.
I still have my youngest DS at the local state. He's ok. He has a different personality and keeps to himself. But, I don't look at the school with rosy liberal glasses anymore. It has huge problems.
Were I to do things differently if I went back in time. Probably, but we do the best we can with the options before us.
It sounds like you have two really good options. If money is an issue, start in the state sector for the early years. You can always change. IME it really doesn't make much difference academically. Children usually get into the same schools they would have gotten into regardless of what primary school.
Feel free to PM me.