That does not sound like a clicking axle to me - far too 'deep' in sound.
Sounds to me more like the cogs in the diff engaging but as you say it seems brake related and is less noticable when the handbrake is off, so not sure.
If your car is still in warranty go back to the dealer.
If not, post up your whereabouts and we can point you in the direction of the nearest specialist for an informed opinion.
Oh and BTW, welcome to the forum and although I'll leave this post here you may wish to put up an intro and another post related to your issue in the 370 technical section.