I highly doubt that. But luckily, I won't be here to see whether I'm right or wrong.
Maybe in some major cities where the roads can be "modernised" to accommodate them in a safe way, and maybe some major trunk roads and motorways. Places where you can rule that every vehicle on those routes has to be self-drive/automated.
But there's no way that we can afford to update every road and lane in the country to accommodate them in a safe way nor have a system where driverless cars share the road with older/driven cars. The costs of changing the road infrastructure and providing the necessary guaranteed/secure communications they'd need would bankrupt the country.
I can see it if we ever start building "new towns" again, or new motorways/toll roads, but there'd need to be restrictions as to which types of vehicles can use it, to either only driverless/automatic, or those alongside "driven" cars with built in automation for communications etc.
To make driverless vehicles work, they have to be able to communicate with each other. Reliance on cameras to look for other vehicles is too dangerous and too unreliable. They need to "talk" to each other so that they know exactly where other vehicles are in proximity to them, and know where other vehicles are changing speed or direction etc.
We're not even close to being there with railways at the moment, which are far simpler as they are in a protected/closed network and limited to tracks etc, far reduced risk of obstructions, pedestrians, etc., and far fewer in number so in theory a lot easier for them to automatically talk to each other when changing speed etc so in theory could run far closer together than the 2/3/4 mile apart they currently have to run. You could even use tech to get them to couple automatically on long runs and then split again closer to stations/junctions. But we're nowhere near doing any of that, so doing it for road vehicles is many decades away.