The venue has a capacity for 100 people and can also be quickly turned into a retail outlet. It has previously hosted Fryars' album launch, a meet and greet session with Finch and the Relentless Kerrang! Awards nominations party.
The NME was founded in 1952 in the building, which is located on a street famed for its musical significance.
Sam Grant, Relentless' marketing manager, said: "Relentless's connection with music has been strengthened over time through innumerable gigs, events, films, publications, partnerships and initiatives to support music culture along with the musicians and fans that fuel it. The future will only see this shared obsession strengthened further.
"We are excited to have a venue that can help provide a platform to aspiring musicians, as well as further establishing the brand as part the British music scene."
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