As mnot said, correlation is not causation and there are many factors involved. There are people who have attended universities that aren't so prestigious who have gotten jobs at FAANG. However, I was curious so I decided to check LinkedIn for the most represented UK unis attended by people working at FAANG companies in the UK (I only included the top 10 for each company to not make it too long, and I filtered for Engineering roles only, as I'm assuming you wouldn't be interested in the non-CS roles like Marketing or HR).
Meta: Imperial - 104, Cambridge - 74, Oxford - 67, UCL - 54, Edinburgh - 29, Manchester - 27, Bristol - 27, Warwick - 26, Southampton - 22, KCL - 21
Amazon: Imperial - 144, Cambridge - 93, UCL - 88, Edinburgh - 82, Manchester - 75, Warwick - 61, Open - 55, Roehampton - 50, Southampton - 48, KCL - 46
Apple: Imperial - 63, Cambridge - 53, Manchester - 26, Southampton - 32, Edinburgh - 30, Oxford - 25, UCL - 21, Nottingham - 17, Warwick - 16, QMUL - 15
Netflix: Not relevant for the UK
Google: Cambridge - 117, Imperial - 113, Oxford - 69, UCL - 46, Manchester - 42, Edinburgh - 32, Warwick - 30, Southampton - 27, KCL - 25, Open - 24