The most likely cause of this is a Diesel Particulate Filter (DPF) that is either blocked or on its way to becoming blocked and needs cleaning. Soot build-up in a DPF can restrict the flow of exhaust gasses, at which point you might also find the car’s computer will limit performance to avoid doing damage to the engine.

You can either try to force the DPF to regenerate, or you may have to have the DPF manually cleaned or even replaced.

The other possibility is a problem with the Exhaust Gas Recirculation (EGR) valve which can also become clogged with soot and affect the vehicle’s performance and emissions. Either way a check up at a workshop with the appropriate scanning equipment is necessary.

Conventional wisdom suggests that a modern electronic fuel-injection system is smart enough not to flood an engine when starting., However, experience tells me that sometimes, you can get excess fuel into the engine if it doesn’t fire straight away. However, if you keep trying to start it, that fuel should pass through the engine, and it should eventually fire. So, I’d say your problem is something else.

A mechanic would probably start by checking things like whether the fuel pump is operating, the fuel and air filters, fuel pressure and whether the fuel injectors are pulsing when they should be. Your problem is likely to be a shortage of fuel rather than too much of it, so checking the fuel delivery pressure and rate is a critical step.

There are plenty of things that can cause this, but being a petrol engine with no turbocharger, it shouldn’t be too tricky to diagnose. Any time an engine runs well when warm but struggles when cold, suspicions are drawn to the fuel/air mixture. A warm engine needs a very different mixture to a cold engine, so modern engines have sensors that monitor the engine temperature, the air/fuel ratio and how well that mixture is burning. If any of those sensors are not telling the computer everything it needs to know, poor running can be the result.

But it would also be worth looking at the air intake side of things. An air or vacuum leak into the intake manifold can also cause rough running and hard starting. The engine’s stepper motor (which controls the idle speed) could also be at fault, but could also be the victim of one of those non-working sensors.