Indeed I checked one of his references where he says that it is cars that are the primary reason that CO2 emissions haven’t reduced in the transport sector. The linked article says that it is airlines (increase of 2%) not cars (decrease of 1%).
“Demand for oil was also largely unchanged in 2018 (-0.3%). Within that total, demand for diesel and petrol both saw annual declines of around 1%, whereas aviation fuel was up 2%.“
Even with a tiny change in relative proportions within transport, road vehicles still use vastly more fuel than aviation in the UK. Without absolute tonnage of emissions, and relative proportion of commercial and private, I can't see a way to invalidate his claim or prefer aviation as culprit. It sounds perfectly reasonable and the least controversial assumption from data available: cars are the big majority of the largest fuel user, though commercial traffic may get low enough mpg to emit disproportionally large amounts.