The Future Anomaly Research Centre is the what the Anomaly Research Centre is called in its appearances in the Future. The Future ARC is of course abandoned with human kind having died at the hands of the Future Predators. It still has the old ARC symbol inside and is possibly a home for Predators.
The location of the Future City and the future version of the ARC will never be known, since there's no proof that it was actually located in London. Nevetheless, the appearance of the Gherkin supports the theory that the ARC in the Second Future is still located in London. It is also possible that they knew that the ARC-Cretacious Forest anomaly resided here and they built the ARC on top of it to test their anomaly technology on it such as opening and closing it.
In the Future ARC, the Artefact, the Anomaly Opening Device, and the large touch table computer are likely a result of Cutter's and Connor's research. It seems that now the ARC has full control over anomalies, such as predicting, locking, opening and closing anomalies. This means that the ARC operation must have changed rapidly; the team could just have been there before any creatures went through, and immediately close the anomaly that occurred. Unfortunately, since Helen killed Cutter and managed to get Connor, Abby, and Danny lost (Danny wouldn't have even originally become the Team Leader), this ARC was neglected, and it's technology was lost, along with the second incarnation of the future.
When the original future timeline was changed (Episode 1.6) and the ARC was built as a result (Episode 2.1) this eventually spurred events leading to the future version of the ARC. Sometime after 2009, the ARC created the Future Predators to have them become "soldiers", in an act sanctioned by Christine Johnson. It is possible that Johnson took control of the ARC from James Lester and turned it into a military facility, as she had been working on an anomaly in her own HQ to the Future City. She had Future Predators taken from the future and experimented on, causing their creation in a predestination paradox. The Predators likely turned against the ARC and proceeded to wipe out humanity. (Episode 3.3)
Helen Cutter killed Nick to try and prevent this, however even with his death the events of the Future ARC still occurred because Johnson was the one primarily responsible for its acts.
The building Jack Maitland became trapped in looks similar to the ventilation shafts of the ARC, used by the team to escape Johnson's soldiers in Episode 3.6. Likely, once humanity became extinct, other creatures, like the Larvae and Megopterans took over the site as a hive.
When Danny, Connor and Abby pursued Helen Cutter to the future, they made their way to the ARC to escape from a Future Predator. The building's identity is revealed to them when they find the symbol of the ARC on one of the doors. There they find Helen working on a console, she downloads the Artefact's Matrix to her Anomaly Opening Device to give her a route to reach Site 333, she opens an anomaly to the Cretaceous with the team in hot pursuit.
As a result of the change in the timeline following the creation of the New Dawn Anomaly, the Future ARC, along with the Future City, was presumably erased from existence.
The ARC logo seen on the wall of the Future ARC differs slightly from the one in the present day ARC, though this may be due to the Future ARC's being changed sometime after the present one.
It is possible that the Future Predator did not simply evolve, but was genetically created by the ARC during research, due to Helen commenting "This is where it all starts." This is backed up by the fact it takes millions of years to evolve and during that time all the buildings would have collapsed. It is also possible that the Predators may have been cloned from others caught in the present (Oliver Leek's and Christine Johnson's captives) creating a time phenomenon known to philosophers as a "casual loop" or in simple terms, a paradox.
If one looks closely at the door with the ARC symbol on it, there is some writing underneath which says 'Cutter Building', above the words sub-level. This suggests that Cutter was a part of the Future ARC's construction along with Connor, or it was named after him.
The second ARC seen in Series 4 and 5 is not the the Future ARC. The Second Future, time period of the future ARC was neglected, along with anything found in it when Christine Johnson died. The Series 4 ARC was built when Connor, Abby, and Danny disapeared into the past.