She is believed to have hit the wall of a bridge in the accident on Tuesday afternoon in Lanjaron, Granada.
Ms De Abreu, who had recently returned to London after living in Cape Town, had been visiting her aunt Gabriela in Spain.
British Foreign Office officials confirmed the death.
It added it was “ready to provide consular assistance”.
It is not yet clear whether she was bungee-jumping on her own or as part of an organised group.
They are exploring the possibility that there was miscalculation with rope, a spokesperson for the Guardia Civil said, according to the New York Daily News.
A spokesman said: “We are liaising with the Spanish authorities and have contacted the family to offer support at this hard time”.
Spanish police are investigating, but a local paper claimed her rope was unbroken, suggesting the height of the jump or the rope length may have been miscalculated.
The Tablate bridge has a drop of 80 metres and is a popular bungee-jumping site used by several adventure sports firms.
One is a modern bridge from which the bungee jumps are launched, with an ancient Roman bridge underneath.
Bungee jumpers fall for about 20m and swing underneath the bridge, with a first jump offered for about 35 euros.
It is considered the gateway to the region and is famous for its mineral water which is sold throughout Spain.
Following her death, De Abreu’s father described her as a “beautiful young woman”.
There is another bridge below which is about 40 metres from ground level.
The area is popular with expats and the hippy village of Orgiva, where people with alternative lifestyles from all over the world congregate, is close by.