Peugeot 106 engine stutters, particularly when cold?

Hi guys and gals. My GF's 1999, 80k(ish) miles Peugeot 106 has been stuttering a little bit for maybe a year or so now, but it's getting worse now winter is kicking in. Basically as you accelerate it drops for a split second then continues, as thought it's missed a firing. This can turn into a juddering sensation when cold it misfires that much.

She swears it gets better after a service, but each time it comes back, so it doesn't really sound like plugs to me.

What would you guys suggest? Something to do with fuel system perhaps? I'm only a novice, so just a guess.

Thanks in advance for tips!