JAM,
The dashpot springs are there for one and only one reason. They are to prevent the piston reaching full lift before the engine reaches full RPM.
If the piston reaches full lift before the engine reaches full RPM then the mixture will not be adjusted correctly for increasing RPM. ie the needle cant rise any further.
The springs tend to fatigue and lose their strength over time so should be tested and replaced regularly when necessary.
There are several springs with different rates.
The general rule of thumb is large engine-small carb=stronger spring, small engine-large carb=weaker spring.
It would seem that whoever replaced the springs in the past didn't or couldn't get 2 springs the same. They are colour coded on one end and it doesn't take much for the colour to disappear. Twin SU carbs should have both springs the same. For Cooper 'S' and Clubman GT with 1 1/4" SU's they should be RED.
The strength of the different springs varies from 2 1/2 oz to 12 oz at the test length.
RED should be 4 1/2 oz at a test length of 2 5/8". To check borrow the kitchen scales and get a piece of tube that the spring will fit inside and cut to the test length of 2 5/8". Put spring in tube and place on scales. press down on spring until it is compressed to length of tube and read scale. This is strength of spring at test length.
The damper controls the rate at which the piston rises as engine speed and vacuum changes. (It doesn't do anything when vacuum drops and allows the piston to fall immediately) This is the "SU accelerator pump" to give a richer mixture during acceleration. It depends on the oil in the damper to control the action. This is why you get a flat spot on acceleration if you don't keep the oil topped up.
Edit: In the dim dark past SU pistons came in different weights and most/all? didn't have springs. Hell of a lot cheaper to have one piston and a selection of different springs to achieve the same result.
Hope this helps
RonR