I am not sure that Westminster figures quoted are that inaccurate. If you look at the link, 86 pupils out of of 201 went to Oxbridge, whilst a further 18 went to elite US schools.
The pattern is not that different to DCs years, a decade ago. Impressively DD's year had eight Harvard acceptances, which was the highest of any school in the world that year, even in the US. The cohort included one of her friends who rejected a Cambridge place in favour of the chance to take a join honours.
If anything Oxbridge was played down. Instead pupils were encouraged to do their own research, with a day off timetable in Yr 11 to look at possible University courses to then inform their A level choices. If the Courtauld had the best course, great. The link shows that, as then, very large numbers went to London (57 this year, including 23 to Imperial and 22 to UCL). Staying in London after a schooling in central London was not idea, but the priority was finding the best course.
What they were encouraged to do was to treat it as a two year process, and apply for the most suitable courses for them. This was important for DC who were aiming for medicine and economics where having the right grades does not guarantee an offer. As @ofteninaspin suggests, economics courses vary and LSE is probably the best fall back for someone aspiring for Cambridge. Both are a bit of a lottery, even for very strong applicants, so add UCL, Warwick and Imperial to the mix.