I'm glad so many people willing to help here
Just elaborating further shouldn't the formula for Zs be taking the form Zs=Ze+(R1+R2)-R2p where R2p- resistance of parallel paths to means of the earth. Since introducing parallel paths in real word reduces the measured value of Zs. Logically I'm imagining some of the fault currents taking the path to means of the earth via bonding hence understandably measured impedance of loop path to the transformer because of some current going the other way to be reduced.
Stop and think again what are you verifying the Zs reading for??
i.e. You are designing or altering a circuit..
Key objective is to make sure that in the event of an earth fault the MCB will trip fast enough to prevent danger.
This being verified by compliance with the Max Zs given in BS7671 tables (or manufactures data).
So you design a circuit with a supply -> A protective device -> A length of cable -> A load.
You don't specifically 'design-in' any parallel earth paths, that may or may not crop up later due other equipment that gets connected to the circuit..
AND.. parallel paths may change over time due to alterations by other non-electrical related services..
(Customer has the heating system replaced / an old water tank and immersion heater are taken out / some pipes in the property are changed to plastic etc..)
You must prove the integrity of the "Electrical installation" part of the earth loop path to be good, sound and intact.
So providing your new/amended circuit has an acceptable Zs by measurement or calculation of (R1+R2) and Ze,
then you can sign your certificate to say the circuit complies with BS7671.
If you based your Zs around some parallel paths that 4 months later are disconnected, you could be leaving a potentially dangerous installation.
But..
If you have a Zs verified by Ze+(R1+R1), the installation remains safe even if someone comes and adds a whole bunch of parallel earth paths two days after you've been there doing your testing.
Bottom line is Zs verified for all circuits, appropriate protective devices, and correct bonding your installation should fail-safe...
and you can sign your bit of paper with confidence.
Guinness