I'm cynical but suspect there are other reasons they will want classics off the road or limited, and possibly that is polution and fuel supply. Maybe he was playing devils advocate and he's a classic fan and wants to see them still in use for as long as possible.
That's more likely to be the reason - you simply won't be able to buy petrol. Even if it's not legislated, once the vast majority of cars are electric, there won't be a need for a network of filling stations or refineries, so there won't be any petrol to buy...
There are two big problems I see with the whole autonomous/electric car thing.
The first is the batteries - current Lithium-Ion technology uses a lot of rare-earth metals. We don't have any of those*, so we have to buy them from China - it won't be long before China says "actually, we need them all ourselves, so we're not going to sell you any", and then we're screwed. We need to either develop new technologies that don't need fresh raw materials, or get very good at recycling, very quickly. (If anyone thinks that won't happen, note that China have already refused to take any more of our waste...)
The second problem is that these automated, hire-on-demand technologies are all geared towards urban areas and motorways - How will an automated car cope with a filthy slurry-covered country lane in January? Where will the "car on demand" come from if you're in a small village or farm an hour's drive from the nearest town? What if you need to lug a bootful of tree cuttings to the tip?
They may be a great solution if you live in the middle of London, but then if you do, you've got a great public transport network already and so don't need a car!
* there are no sources of any of the key rare-earth elements anywhere in Europe.