University bias doesn't exist. Contextual offers exist where students from certain deprived postcodes from families on benefits at schools which send hardly anyone into higher education, yes, those kids predicted 3A's are going to be judged as higher achievers than a kid predicted 3A's from a grammar or Indie with middle class parents in a middle class area. So it has no bearing on your decision, unless your third choice is to move into a council house in a deprived area and send them to underperforming school which sends hardly anyone to Uni.
Your decision is simple, pay over 100 grand or pay nowt. Some grammars have superior A level results than some private day schools, you need to judge the school on RESULTS , AND if you are willing to invest over 100 grand into your DC's education, 200K + if you have more than one.
Its hardly a dilemma, if the grammar has better results, its a no brainer, if they have the same, then it comes down to cash, if the Indie has better results, then its the cash again- can you really afford it, have you got good provision to pay for it- i.e if you're paying from salary, you have serious wealth in savings, investments, if the answer to the simple question, if you never work again, could you afford to keep them at school, is yes, go for it. If its a no, you have to reconcile that before sending them private- its a cash drainer and very hard to get out once you're in. ( My kid have been in private school since 3+) It has cost us a fortune over the years and with fees, the only way is up,