Engine shaking when cold

I've got a problem with my Peugeot 206; 1.4l Petrol, 55 plate, 32000 miles.
Basically when I start it up from cold, I leave it for about 30 seconds and the engine starts to shake and jolt a bit and the revs go up and down ever so slightly. If I try to accelerate its like its trying to pull away but cant and jolts a lot even with my foot all the way down. Sometimes it backfires as well when trying to accelerate. Once the shaking is done it runs fine and wont do it again unless I turn it off for a couple of hours and start it up again. I've had it down a garage and they've cleaned out the filter and run an engine diagnostics test and said nothing comes up that suggests theres a problem but it still does it. Was hoping you could shed some light on this as to what it might be? There seems to be quite a few people with this problem but with lots of different recommendations.