My parents used to say: going to a good school is not only about good teachers, it is about good classmates. That matters enormously.
I did not understand it then. I do now.
What happens when you look around
Set aside family resources for a moment and consider only the environment.
Walk into a high-achieving school and look around: in year ten, band 7 is unremarkable. Band 8 is unremarkable.
At an ordinary school, 6.5 is considered hard.
What that does to you
When 7.0 registers as normal, you will push for at least 7.0, or 8.0.
And later, studying abroad feels ordinary too, because everyone around you is doing it.
This is what a limiting belief is
English has the term limiting beliefs: the ceilings we quietly install in ourselves.
In an environment where everyone reaches a certain level, your ceiling sits higher. You stop asking "could I do that" and start asking "when will I do that".
In an environment where nobody does it, the thought of trying may never occur to you.
If you are not in that environment
You can still choose your environment. It just takes more deliberate effort.
Choose who you follow. Choose which groups you join. Choose a class containing people at the level you want to reach. The ceiling in your head is built from what you see every day, and you have some say over what you see.