Meh you need to broaden your horizons (or LinkedIn stalking skills). Plenty of local uni, non-oxbridge UK unis at these firms too.

One trick is to move into comparable / peer firms if you think you’re being screened for having low academic credentials. This is why Baker has some allure - US / UK firms know the brand (even if the operate differently from the US / UK). As people burn out / move, your opportunity will come to join these stepping stones.