mummytime "if they went to a State school, they are slightly more likely to get a higher classification of degree. Therefore, sending your DC to State school you save the fees, and they get a better degree"
No - this is a common garbling, but it's nonsense. There's not a shred of evidence that if you choose to send your child to a state rather than an independent school they are more likely to get a higher classification of degree. What there is is evidence that if you take a state and an independently educated child with the same A level results then the former is slightly more likely to get a higher classification. (Only very slightly, mind, at the top end: iirr, you're already overcompensating if you drop an offer of BBB or above by 1 grade in 1 A level for the state school child.)
We can't randomise children at birth, but the plausible result of the thought experiment where you separate your identical twins and send them one state and one independent is that the independent school child gets a better chance of good A level grades, and a slightly better chance of a good degree, than the state school child. It's the drop from "better" to "slightly better" that gives the results observed when you compare state and independent school children with the same A level grades. The independent school gives better results, but less than 100% of that advantage carries through to degree level. Surprised? You shouldn't be.