Just an update...
I have found something which looks absolutely perfect for my needs: Adafruit 16-Channel PWM / Servo HAT
The only problem here is most of the peristaltic pumps I've seen are all DC motors and not these 3 wire servo motors that are required for this motor driver board.
Do you think it would be possible to wire DC motors to that servo HAT, if I did 1 positive and 2 negatives?
After further thoughts on the design of the liquid dispenser - it would be nice to be able to change the direction of the motor, so that the liquid that remains in the tube can be moved back to the reservoir (this is not essential, as I could manually put the liquid back in by disconnecting the tube from the reservoir, running the motor until tube is empty and place the liquid back into the reservoir by hand).
It may be that I convert some cheap servo motors for continuous rotation - which I have seen somewhere recently, then engineer my own peristalic pumps with the 3D printer. Then I could utilise the 16-channel connectors on the servo hat.
Do you think after modify the servo's that I'll still be able to change the rotation?
I'm very likely over engineering a simple task that can be achieved with a small number of parts on a breadboard (e.g. ULN2803: 8 Channel Darlington IC).
Anyway, I think best I continue to do more research into this, as if I can build a 16-channel DC motor driver which allows switching direction, that would be ideal as I wouldn't need to create my own peristaltic pump and mod a servo, etc, etc.