Steam
Is the wiring getting very hot rapidly Yes or is it getting warm, going to hot as time goes on and is it the same at the switch as at the lamp connectors? Yes
Is the wiring at the stalk also going the same? I haven't checked that aspect.

This would suggest you have a short or an incorrect connection(s) rather than on overload problem. To narrow down and track where this may be you need to work through the wiring methodically an divide and conquer the fault or faults.
To start if you disconnect both connectors at the headlamps, preferably at the actual lamps but at the bullet connectors where the lamp wiring joins the main loom will do and then see if it still gets hot. If it does then the fault is in the wiring to the switches or the actual switches. If it stays cool the fault is at the headlamps and you can work forward.

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Cheers Dave.

Steam Do you mean the bullet connectors at the front of the car or the lamp connectors?

Either will do, we are starting at one end point, if the lamp connectors are too hard to get at then the bullet connectors next to the grille.

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Cheers Dave.

Just been playing with front parker flasher lights and found that the black earth wire can be removed as the L594 unit is already earthed to the body by the mounting screws.

Cooperess,
You say that "Low beam is on the switch and high beam is on the stalk". This is not how the car is normally wired.
For Clubmans.... if that is your car.
The "headlights" switch on the dash connects the power to a blue coloured wire (labelled U) that then goes to the "dip switch" part 23 of the stalk. The stalk dip switch then "chooses" to send the power to either the High beams (blue/white) and the light on the dash OR to the Low beams (blue red). Your wiring loom might? use these colours.
You will have to get to the connectors on the stalk and check the in and out voltages AND how hot they get.
I can just remember my Morris 1500 in the 1970's had a blinker/headlight stalk but with the "flasher" not connected. (It was probably from the same parts bin as the clubman).
Good Luck. Dave 2

The screws holding it in place are not a reliable earth.

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1986 Mayfair (998 auto), 1974 S, 1974 Van, 1972 PMG Van

Too many minis

Even through there are 3 screws on each side! Also I see the new replacement parker/blinker seem to only have 2 wires.

Done some multimeter tests.

If I put 1 lead on headlight blue/white, I get continuity on cars wiring on blue/white and black, Could this be the heating of wires.

That will depend on what you have disconnected. The continuity will be through the headlamp globes or through the high beam indicator lamp.
Did you disconnect the headlamp wires at the bullet connectors yet?

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Cheers Dave.

The readings I got were from the lamp socket with the bullets connected to the main harness.

I posted this a couple of days ago as a start to walking you through a fault finding process.

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Cheers Dave.

Thank you David. That doesn't explain continuity between the main wiring loom blue/white and the black wire when one probe is on the disconnected light socket blue/white wire with battery disconnected and key and switches turned off.

The high beam indicator lamp is still in the circuit.
If the wiring is still getting hot when switched on and both lamp units are disconnected then the fault is in the switch/stalk/wiring loom. If it does not get hot then the fault will be in the lamp looms or connectors.

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Cheers Dave.

I have decided that if I keep testing with the new loom connected, just to see if the wires get hot, I will wreck the new loom. There must be another way of doing these tests, so the loom is not wrecked, if hasn't been wrecked already.