09 1.2 lower revs stutter

Had this issue ever since I bought it a year and a bit ago, but it comes and goes. I wonder if it's weather related, as it's been performing like it's a 1.6 in the recent dry hot weather, and then today, misty, damp and cold (autumn in April) it's started doing it again with a vengeance; but not right at the off, only after driving into town and then a brief stop. Probably never fully goes away, but it does seem variably noticeable. Might also be more noticeable when more weight/people in it?

Basically, at around 2.2-2.8k revs it's stuttering or hesitating and reluctant to pull (whether under hard or soft throttle, slow or attempted hard acceleration, hill or flat). No other symptoms, and once past 3k it's fine. Being as how I usually drive it on country lanes, and it needs to be kept high in the revs to pull up and round the hills & bends, it isn't a huge problem - until I have to go onto slower or A roads or into town.

Happens in all gears, cold or warm. Doesn't seem to be specific fuel or filling station.

If it was a motorbike with carbs I'd be looking at idle screws, pilots and/or main jets (i.e. low end fuel/air mix - somewhat used to this!) - but I know nothing about 'clever' modern cars...

Could it be plugs? Leads? Fuel management system (or whatever the car has)?

Does it need diagnostic plug-in testing/fixing stuff or what?

Car has about 65k on clock.

Cheers for any ideas or advice.