Absolutely. Cambridge usually require A*AA for Philosophy.
Please note that their website says that Churchill, Corpus Christi, Lucy Cavendish, and Selwyn sometimes require more than the above. I notice that none of those are particularly posh in private school percentages. According to The Tab, 24.2% at Churchill were at private school, 23.8% at Corpus, 18.9% at Selwyn, and just 7% at Lucy Cavendish. Churchill, despite being a young college, states some strong connections to the Philosophy Dept and says that it has a generous number of places, although doesn't seem to say how many. Corpus accepts 2-3 Philosophy students a year and they say that they have a comparitively large number of Fellows interested in Philosophy, for a small college. Lucy Cavendish accept 2 a year and their website doesn't say why choose that college for it. Selwyn accept 1-3 a year and their website is enthusiastic about the subject and their proximity to the Sidgwick site where Philosophy lectures are held, yet they equate Philosophy, (the supersubject!), with being a 'smaller' subject (?).
Cambridge are famous for not caring about GCSES as much as Oxford or some other high ranking universities. It possibly originates from Cambridge's more left wing stance about giving 'late' bloomers a chance to shine beyond the usual outcomes of which secondary school they happen to have attended. There are no GCSE requirements stated on their website for Philosophy. Cambridge nearly always 'make up for this' by requiring the very highest, or joint highest, minimum A Level grades of any UK university, usually slightly higher than Oxford's. However, actual A Level grades achieved can be very different at such famous, prestigious, places, and Oxford is very well known for Philosophy in its own right. Average A Level entry grades achieved by entrants for Philosophy are currently 100% at Oxford and 92% at Cambridge, according to The Complete University Guide.
Despite Cambridge's reputation of 'positive' discrimination towards state school applicants, the 2 Oxbridge colleges with the highest percentage of private school students are at Cambridge, Hughes Hall on 70% and Trinity College on 47.3%.
Bertrand Russell, A N Whitehead, G E Moore, and Ludwig Wittgenstein, studied at Cambridge University.