Johnson (1930) 'The Nature World of London' does not mention Sparrowhawks, but says of kestrels (largely predators of birds in urban areas) "the evidence points to the existence of many individuals, which continue to live amongst us [in London]".
Lilford (1895), Sparrowhawk: "very common in the Peterborough area".
Chislett (1952), Yorkshire, Sparrowhawk: "there are areas near to large towns where Sparrow-Hawks suffer little molestation". Second only to the Kestrel in abundance (Nelson 1902).
Chislett (1952), Yorkshire, Kestrel: "can often be seen hovering above rooftops in many lowland towns".
Hudson (1924) 'Birds in London' describes massive predation on London sparrows by cats, which he often witnessed destroying whole broods shortly after fledging, and with injured birds being common in the parks.
So it appears that predators were not absent from London prior to the 1990s. These predators were avian (Kestrels at least) and mammalian (cats). Yet Hudson counted 118 sparrow nests on his walk through a London park. So 'predator aversion' must have also been present at that time, yet they were still super-abundant.
Sparrowhawks were clearly present about other large towns prior to 1950, as were Kestrels, but again sparrows were still super-abundant.
So CPBell's theory would require sparrows to lose this predator aversion in the 20 years between about 1960 and 1980 when predation from raptors was rare due to organochlorine poisoning (but note that cats would still be present in London and other towns, so sparrows would still need to be wary - in fact the cat population has increased), but not having regained predator aversion in the 30 years since 1980 and rebounded back to their former numbers.
That doesn't sound very plausible. If they can 'unlearn' something in 20 years then why can't they 'relearn' it in 30?
But as CPBell he says, he is "assuming" that this ever happened. Just like he assumed that no house-building happened between 1970 and 2000 in his model, the whole idea of a house of cards. The empirical evidence clearly shows he is wrong - from house-building spikes and urban sprawl in the 1970s and 1980s to the presence of urban raptors prior to 1990.