A driverless taxi *would* be cheap. That's the whole point of them being driverless. It should be cheaper than owning your own car as the fixed cost of ownership is spread across all the users. There would of course be a profit margin for the operator, but that would be vastly lower than the cost of paying a human.
It would still depend on usage.
For someone doing (say) 4,000 miles a year, the certainly it should be possible to get the cost down to around 60p per mile so that it was at least comparable (although it's worth noting that's at least 1/2 the cost of the typical £1.20-£3 per mile taxis currently cost).
However, for someone doing (say) 20,000 miles a year it would still likely be cheaper to open their own car.
What might be viable is a vehicle with a few pods, so that more than one person could use the vehicle at a time. You might find that your have to divert from the most direct route to pick someone up or drop someone off, but in exchange the cost is reduced. If the cost had typically got to that 60p per mile rate, by offering to "share a route" you may only pay 45p per mile (of the most direct route), in doing so you save money, but the operator gets the potential to make more money by earning more per mile (although this is likely to be reduced due to diversions, not always being able to fill the other half/the other two thirds, and higher vehicle costs).
For example, a MPV typically has 3 rows of seats, given most cars on the roads have one person in them (with quite a lot which have more than one person only having two), and mostly only carrying a limited amount of stuff out shouldn't be that complex to create a vehicle with 3 zones, each with two seats and a bit of space for (say) a few small backpacks.
The other advantage of such a vehicle, is that it would reduce the number of vehicles needed to provide peak capacity. This has two main advantages, firstly the extra cost wouldn't be as much as twice the cost of a standard vehicle (so cheaper to provide peak capacity), secondly it would take up less road space than three vehicles and so would mean that there was less congestion, which would mean fewer vehicle minutes in operation to move the same number of people.