Ivy contains saponins which are steroid glycosides (see the Harmful Properties section of this website) and falcarinol, which is capable of causing allergic skin reactions, so this plant is one to avoid. It is a commonly grown cultivated plant in the UK but can often be seen growing in the wild.
Ivy growing along the ground and up walls makes a great ladder for tortoises to climb, so always clear any Ivy away from the perimeter of your enclosure to prevent your tortoise from escaping.
N.B. Do not confuse with Ground Ivy (Glechoma hederacea /Nepeta glechoma) or Boston Ivy (Parthenocissus tricuspidata).