White smoke and pressure in radiator.

the HONDA Horizon (Isuzu wonder box)
what engine. exactly .?
3.2 L 6VD1 SOHC V6
3.2 L 6VD1 DOHC V6
3.5 L 6VE1 DOHC V6
3.0 L 4JX1 TD I4
3.1 L 4JG2 TD I4
x1 or G2?

floods, wot cranking cuts fuel and starts any flooded engine,
it's overheating that wins the First order failures rule sets.
nothing else matters. cure that first.! find cause! first.

sounds (im deaf there,lol) that smoke is out tail pipe end and dissipates fast and is not smoke but steam, , oil smoke smells like burning oil and lingers. steam smells sweet like burning Antifreeze.
AF steam is a blown head gasket or far worse.
do a compression test first to see if it's even worth fixing????
most are NOT. (unless free labor, sure)

first learn steam from smoke
serious , watch moms tea pot. see that steam goes away fast.and very uniquely , now watch burning oil.
remove dip stick, drop the drip of oil on hot exhaust manifold.
smell that, that is oil burning, and lingers.
this will last you a life time of blown engines..... just one look and bingo. (my instructor in 1965 did in front of class)

got oil in the AF/ CARBON chunks in same.
water in oil, ? pan, engine . milky oil.
rad leak down test fail? can be lots of reasons even a cracked block.or head. not just gaskets.

I assume you mean if you want to rev it up you get white smoke. White smoke is water or coolant getting into combustion chambers. This often means head gasket problem or crack i head or block. You can use a pressure testing device on the radiator to diagnose a leak, but also check for water in the oil or oil in the water. Good luck, I think you have big problem.

It`s a diesel Engine no spark plugs.
More than likely it is your injector seals .They have to be replaced

If you have white smoke coming out of the exhaust after the car warms up then you have coolant getting into the cylinda white smoke after start up when the engine is cold is normal intill everything warms up

If you need further help, I’m available over the phone at https://www.6ya.com/expert/edward_020b3320326d263d

Could be that the hoses are just old and weak. There is supposed to be pressure in the system when the engine is hot. Squeeze the hoses in different areas. Do they feel softer in certain areas? If yes then replace hoses. You could also have a blown headgasket (even if you don't see white smoke). Let the engine run for a while and see what happens with the temperature. Let me know what you find out and I will continue to help.

indicates a fuel supply and pressure problem
check and bleed the system
have the injectors professionally overhauled by a diesel specialist shop

White smoke is usually a sign of coolant burning. Carefully open the coolant cap, sniff the inside. If there is an exhaust smell you more than likely have head gasket problems. A further diagnosis is needed to be sure. Also ensure that any wires/plugs are reconnected. If the oil sensor is unplugged the vehicle wont start.

difficult to diagnose ,would need to put a pressure tester on radiator and see what happens as white smoke is water vapour,unless its diesel as people often describe white smoke buts its a light grey which is fuel ,although the question does say TDI so am i to assume its a diesel turbo injection ,if it is then to think some more i would need to know if it has an injector pump or if its common rail .because you can have two completely different answers

was it over heated? may need to check for blown headgasket or leaking water pump

my 1988 chevy blazer 4x4 smokes on cold starts till it warms up then it goes away what is causing it