So, driving in neutral, does it save on fuel?

Provide solid evidence otherwise you're just using words like me

Maybe

Here: see 122 on coasting; not against the law but advised against.

https://www.gov.uk/general-rules-all-drivers-riders-103-to-158/control-of-the-vehicle-117-to-126

Really? Sitting with your foot on the clutch is one of the most idiotic things one can do?

As opposed to not checking the mirrors, driving in the wrong lane, breaking too suddenly, taking corners too fast, speeding, overtaking unsafely, ignoring road signs, doing your makeup in the back mirror, approaching a roundabout too fast, jutting into the road when you're trying to pull out into traffic, being drunk, feeling tired, driving without functioning lights, failing to indicate, cutting in front of someone, tail-gaiting...

Coasting is safe under the right conditions. Avoiding coasting is not a driving priority. I have never experienced any sensation of loss of control in relation to coasting, presumably because I do it at the right time and in the right way. You "coast" for a few moments every time you change gear, does the car spin out of control?

Seconded
Even my instructor said that coasting is beneficial at some times. She used to encourage me to coast around particularly sharp corners as 1st is too slow an 2nd is too fast so she said...in that kind of circumstance you should engage the 2nd gear about half ish which will give you the right speed.

Your instructor says some worrying things. Coasting around sharp corners is the best way to ditchfind.

I love this idea some people appear to have that putting your foot on the clutch will make your car suddenly swerve uncontrollably off the road.

Seconded
Even my instructor said that coasting is beneficial at some times. She used to encourage me to coast around particularly sharp corners as 1st is too slow an 2nd is too fast so she said...in that kind of circumstance you should engage the 2nd gear about half ish which will give you the right speed.

Also coasting is needed when your stuck in traffic.
It all depends on the situation and mindset of the person who is coasting!

Really? My instructor told me to avoid coasting around corners at all costs because steering isn't great.... :/

what exactly happens in the engine when you drive in neutral?

So if I drive down a hill for example and take the car out of gear and put it in neutral is it true it saves on fuel?

Your instructor says some worrying things. Coasting around sharp corners is the best way to ditchfind.

Here is a better explanation

My instructor's car was a diesal :

A diesel car in 2nd gear will pull along at 10mph approx. This is too fast for a tight left corner major to minor. So feet off is going to result in a turn which will be too fast. Therefore try braking to slow the car down produces a judder from the engine and the torque which is pretty strong in a diesel will resist the car being slowed down. The answer is to slip the clutch. Allow the engine to return to tickover with a slight pull from the slipping clutch. That is good clutch control not poor car control.