If a number of installations are connected to a single phase distribution transformer such that their respective loads cause successive voltage drops in the distribution cable, will a short circuit in the last installation on the distribution line be affected by those voltage drops? In other words, will the fault experience the open circuit voltage of the transformer or some proportion of it?

The fault will "see" whatever the supply voltage is at that point, i.e. the open-circuit EMF less the voltage drop along the distribution cables.

For calculating prospective short-circuit current however, you would need to use the full voltage, as a short at the far end could occur when no other loads are present.

Hi Paul,
Thanks for your quick response. I am actually interested in the lowest fault current for earth loop calculations. You see I would agree with your good self but a seior and may I say well respected engineer in the power company insists that this is effectively a Thenevin equivalent circuit and thus the fault will experience the open circuit voltage.
I measured 190v at the terminals of a pme single phase installation. This voltage varies over time. The Zs of some circuits is close to maximum tolerable values and such voltages give me cause for concern. Now I know that it is not the terminal voltage that drives the fault current but I am convinced that the upstream loads will affect the value of earth fault current?

The fault on the end of the distribution line will certainly have an effect on the current drawn by loads closer to the source as well. An example: If you had a line with a total reistance of 0.04 ohm (and ignoring the source impedance of the transformer), then a dead short at the far end would give rise to a fault current of 6000A. An installation tapped from that line at the 75% point would see a terminal voltage of 240 - (0.75 * 0.04) * 6000), or only 60V, so at the moment of the short occurring the current drawn by installations upstream will certainly drop.

But back to the main point, if the loop values are already close to tolerance, then if the voltage at the supply terminals of the installation is low due to other loads, the short-circuit current may be too low for protective devices to open in a timely manner.