The link you provided there agrees with me.
"A landowner who confronts you whilst trespassing on his land is unable to confiscate the contents of your basket, as they belong to you. However, you still must leave the land at the earliest opportunity."
It's legal to go into your garden and pick mushrooms (from a theft point of view) if I want, though the entering of the land is in itself trespass. The going into your garden would be trespass, which is a civil offence and you'd have the right to ask me to leave which I would have to do. However, if I picked mushrooms you would not be allowed to take them back, they would legally be my property at that point.
Section 4, subsection (3) A person who picks mushrooms growing wild on any land, or who picks flowers, fruit or foliage from a plant growing wild on any land, does not (although not in possession of the land) steal what he picks, unless he does it for reward or for sale or other commercial purpose.
The trespass is not lawful, but the foraging of fungi/berries/leaves is as long as they're not being uprooted.
We are moving off topic - but I'm not sure there's much more to say about the access land
The law also says you must not cause damage (which is a criminal not civil offence) - one would have to be careful that damage is not caused. For example, my land is managed completely for conservation and there are signs saying that. Consequently, I could argue that the removal, or even the movement, of material was a damage to my efforts, costs, and plans for the land. I appreciate that if there is no conservation management plan there would be no claim of damage; but with the published plan being specifically to improve biodiversity any disturbance could be argued to be damaging. Luckily I've not had to test this in court