The Op's post is rather misleading because it doesn't tell the full story.
The majority of places in independent schools will always be for fee payers - those for bursary students,me specially those on really significant ones will always be very small in number.
The majority of bursary offers will mean parents still have to pay a chunk of fees, which would make the school unaffordable for many.
High level bursaries are usually linked to performing at a very high level in entrance exams - most children won't be able to do this.
The reality is most children from families who can't afford full independent school fees won't be able to access a suffice t bursary to attend independent school.
That's not to say that some won't.
Perhaps it would be better to say that people on extremely low incomes with e trembly clever children might find their kids can get a full bursary.
Those more in the middle probably would still be expected to fund a chunk of fees making it unaffordable. Those with just moderately bright children probably won't get offered a significant bursary.
I'm not trying to discourage people. There are great opportunities available through bursaries.....but it should be clear that they aren't just available to all who can't afford the fees. They really aren't......otherwise the state schools would be empty!