I have a 2009 TD4 auto model.
Vehicle runs smoothly with perfect gear changes when in motion. When I slow down and come to a stop, the vehicle appears as if it wants to cut out and stall and the revs drop more than they should for about 2 seconds and then it increases slightly to normal idle levels and then runs smoothly again - at this point the vehicle is still in gear. When the revs drop the whole car shakes briefly.
If I put the vehicle into neutral just before stopping, then the low revs and shaking sensation does not occur. It’s a similar sensation to a manual car when you go too slow while still in gear and it’s about the stall.
I initially thought it was the throttle body - I removed and cleaned this thoroughly last weekend but it make no difference.
Any idea what causes this dropping of the revs, which results in the unpleasant shaking sensation.

I'd say throttle body. Did you check the action of the throttle plate was smooth, with no grinding of gears? 2009 Rimini Red SE TD4. Soon to be sold.
Hyundai Ionic 5 Ultimate on order.
Gone. 2006 Tonga Green i6 HSE.

I also hoped it was the throttle body - took it out cleaned it. nada.
The butterfly flap in the throttle body seems to open close fine - it has a bit of tension which is normal. It moves freely and i dont think the gear and broken.
Somewhere i also read it might be a tensioner or pully by the alternator. I need to try that this weekend.
To me it seems like its being starved of air and it feels like it wants to stall. The MAF sensor was cleaned, and there appears to be no holes or leaks in any of the pipes on top by the air intake or from the turbo to the throttle body.
Hoping to take it to a dealer who can do some diagnostics.
Im a bit stumped ?!?

You should also check for an air leak.
I had this issue for many years going on, no one was able to diagnose it, no fault code, throttle body replaced, egr replaced, nothing cured. Then after reading some more on this forum, it was a colleague here who mentioned he cured a similar behavior by replacing intercooler hoses. So I went and did a smoke test and found a small crack on this hose. Plus it looks that the connection was not well made on the air filter box, as after putting it back it almost cured! Who knows who and when worked on this, as I recall having it for so many years! Thanks @Grue again for kindly replying on my PMs two months ago.
If there is a very tiny crack it won't throw a code and will give exactly this kind of annoying stuff.