I have been told that I should shift the gear to Neutral when coasting, in order to maximise fuel efficiency. Is this advisable?
No, it is not. In most modern cars, a high level of efficiency is already attained when you are coasting (moving with your foot off the gas pedal). Shifting to Neutral gear will not garner any perceptible improvement.
In fact, doing so may compromise safety. In neutral, you lose some degree of traction. When you need to make a sudden turn, it may unsettle the car more than it usually would.
Also, you will not be able to accelerate out of trouble quickly when you need to.
You will require an extra second to re-engage the gear, and that second may well mean the difference between life and death.
Cars with an inbuilt coasting mode are able to re-engage as soon as the accelerator pedal is stepped on.