Woody said pretty much what I was going to say. Congestion would be much less of an issue than it is now and of course congestion is only a problem now in cities, the vast majority of the country is congestion free.
In cities such as London for example than your traditional mass transit will still make sense and the replacement of lots of private vehicles with driverless cars using networked route finding would make things much better than they are currently.
Where my idea really excels is outside of the city centres, the places where mass transit is not needed and where even small scale public transport such as minibus services are still not really a viable option. In these places, say rural Cornwall for example, a small fleet of driverless vehicles could give residents much greater independence and freedom than they currently have and at a very low cost both financially and environmentally.