Territory cold start rough running

I had something similar with my Territory. Sounds like a possible fuel delivery issue, maybe even an engine misfire at the start. I'd suggest running an injector test to see if they're spraying correctly. An injector sprays fuel into the engine. If it's defective, it won't spray the fuel correctly, causing cold start problems.

Thanks. By 'injector test', do you mean taking it to a mechanic, or is this something I can check myself? Also, do you think cleaning the fuel system is a possible solution?

While cleaning the fuel system is always a good idea, that might not solve the cold start problem entirely if the injector is defective. For the injector test, unless you have the right tools, it's best to take it to a workshop. They have specialized equipment to see if the injection valve (the proper term for a fuel injector) is working correctly. From what you describe, it probably needs replacing. It cost me around 515€ to get sorted.

That's very helpful, thank you. I will take your advice and bring the car to the workshop for inspection. I appreciate you sharing your experience.