I've never visited Basel, but if it is smaller than London I'm sorry it is simply not possible your claim about their exhibitry is true.
No, it definitely can be true. I also haven't visited Basel, but a British example would be Colchester, who claim to be 24 hectares (60 acres), compared to London's 14.5 (36), but, unlike London, the zoo includes undeveloped space and car park in its measurement. Measuring it out manually with an area calculator tool gives an area of 12.9 hectares (32 acres), noticeably smaller than London.
Yet, Colchester manages to display elephants, rhinos, giraffes, tigers, lions, leopards, cheetahs, chimpanzees, orangutans, sea lions, bears, wolves, pygmy hippos and many more large mammals (it may be the most comprehensive collection of large mammals in the UK, in fact).
The problem is that, unlike Colchester, a much newer zoo, London wasn't built with space efficiency in mind. They accepted a site with a canal and a road in the centre, built several large structures, which are expensive (and now illegal due to being listed) to demolish or rebuild, and have all the remaining open spaces to sparse to be connected for future exhibits. Area doesn't impact the quality of a zoo - management of said area, on the other hand, does.
And, for the record, Whipsnade's existence doesn't make it a pointless comparison at all. For people like us who view ZSL as one entity and visit both regularly, maybe. But if you are an average visitor, you have to pay double the price to visit both zoos, and bare in mind that Whipsnade isn't all that easy to reach by public transport.
You are completely right in saying that lacking megafauna is not a crime. I respect London's focus on smaller endangered species. However, size is certainly not a valid reason as to why they don't house any megafauna.