Manual car juddering when moving off when cold

I have a 2006 Suzuki Swift (Irish registration) which is a 1.3 petrol manual. Recently, when moving off when the car is cold, it is very sluggish, and I have to give it more acceleration than I normally would. And even at that, it moves off slowly, and the car judders relatively violently. When the engine is warm, and the revs have dropped below idle after warming up, it moves off as expected with no vibrations or juddering. I just feel the car is much harder to drive when it is cold. Would this be clutch issues?

Tester

Another idea, engine is misfiring when cold. Cold engine requires richer fuel-to-air mixture, and you may have a vacuum leak that is compounding . Usually that would cause poor cold-engine idle quality and possibly turn on the check engine light. Is it on? I’ve had a vacuum leak on my truck at times and in that case cold engine idle still seems ok, but symptoms occur when accelerating from a stop, stall, or shudder, etc. Truck engine may not be as sensitive to vacuum leak b/c it is 8 cylinder.

I had this happen once when an oil leak dumped oil right onto the clutch. I fixed the oil leak and the problem got better but I eventually had to replace the clutch as the damage was done.

Also, are there any stored codes/check engine lights on? I had an issue with my oxygen sensors cause bucking like I didn’t know how to drive a manual at low speeds once.