In year six, and in a non-denomination school, without a baptism, and without having spent primary school getting a good relationship with Father and the Church, she has NO chance of getting into a good secondary Faith school.
She will be competing with children whose parents have literally washed the Church linen for six years on a voluntary basis, while their children have attended school, and weekly Mass with their parents. The recommendation from Father is pretty much Everything...
It is amazing how many people discover religion when their children are 3 years old, and school applications go in.
I was regular at our Anglican parish church, and in various committees, and doing voluntary work for the Church, but as we had not done this for three years (new to the area, and our sons had a Catholic baptism) we had no chance at the local CE Faith school.
The Catholic baptism was stronger currency than my regular attendance and voluntary work for CE, so ds1 had no problems getting into a RC Primary. (dh is Polish)