Looking at the symptoms it certainly looks like the gasket has blown into the water jacket so pressuring the coolant system. You can get different types of test kits from the likes of Amazon starting at about £20. My advice would also be not to use one of the headgasket repair liquids or your coolant system will probably block.

 

Compression test.
Oil in coolant, coolant in the oil. (ie, brown sludge)
Excessive water vapour in the exhaust and or oil. (oil is weak signal, as can be other things)
Bubbles in the coolant or coolant disappearing.
Excessive temperature when running. (weak signal, can be stuck thermostat valve)
Rough idle or missing (weak signals, as they can be other things).
Hard to start if left for few days or more.

You already hit most of the signals, I would need to be thinking blown head gasket.

 

How do run run a compression test? And is it a factor against that the oil in the engine itself is fine (ie no coolant seeps into to the engine)?

 

Looking at the symptoms it certainly looks like the gasket has blown into the water jacket so pressuring the coolant system. You can get different types of test kits from the likes of Amazon starting at about £20. My advice would also be not to use one of the headgasket repair liquids or your coolant system will probably block.

Looking at the symptoms it certainly looks like the gasket has blown into the water jacket so pressuring the coolant system. You can get different types of test kits from the likes of Amazon starting at about £20. My advice would also be not to use one of the headgasket repair liquids or your coolant system will probably block.

Thanks! Were you referring to one of these kits?

Lisle 75500 Combustion Leak Detector : Amazon.com.au: Automotive

Lisle 75500 Combustion Leak Detector : Amazon.com.au: Automotive

www.amazon.com.au

It’s not immediately clear to me where to stick the tube into - will ask the seller but if you know, let us know please!

 

Thank you all for the helpful responses. My mechanic doesn’t think that the head gasket is blown and strongly suspects that it is a transmission failure. There were some issues with the transmission (delayed / jerky gear switching) prior to the oil being found in the coolant / car overheating. Do you see that this could be transmission failure (coolant gets into transmission)? Something that I need to research, but how is that possible?

 

They make them, they use glow plug. On petrol engines they use spark plug.
example Repco 37 Piece Diesel Compression Tester Kit - RTT8003 - Repco | Repco Australia

How to use it
(465) Diesel Compression Test or Leak Down Test? Toyota Land Cruiser 1HZ 1HD-T 1HDFT 1HDFTE - YouTube
Then if confirmed leak, use a leak down tester like this
(465) DIY Leak Down Test on a Toyota Diesel 1HD-T 80 series Land Cruiser - YouTube


The other option mentioned
(465) How to Tell if Your Car has a Blown Head Gasket - YouTube