The Kelvin Memorial Archive in London was officially a Starfleet archive containing publicly accessible data, named for the destroyed USS Kelvin. It was secretly a Section 31 facility. It was close to Nelson's Column.
In 2259, John Harrison blackmailed Thomas Harewood, who was stationed there, into detonating a bomb in exchange for a blood transfusion to save Harewood's dying daughter. After ensuring his daughter's safety, Harewood walked into work and detonated the bomb – disguised as his Starfleet Academy ring – by dropping it in a glass of water, but not before messaging Admiral Alexander Marcus to explain Harrison was threatening him.
The resulting explosion claimed forty-two lives, including Harewood. In the midst of the chaos, Harrison inspected the rubble and recovered a portable transwarp beaming device. He later used this to escape from an attack he subsequently committed, on a meeting called by Marcus at Starfleet Headquarters regarding the bombing. (Star Trek Into Darkness)
For interiors of the archive, the production shot on a minimal green-screen set, involving performers playing Starfleet personnel. An enormous hall was represented with CGI done by Associate Visual Effects Supervisor Patrick Roos at Industrial Light & Magic's Singapore division, where Roos also generated an explosion that ripped through the chamber. (Cinefex, No. 134, p. 81) The outside of the building was represented by the SB Springs building  in downtown Los Angeles. The words "SB Springs" are in fact quite largely on the building and can be seen in the movie, albeit very hard to read.
In wide shots of London, further explosions were created using ILM's fire and dust solver, Plume. (Cinefex, No. 134, p. 81) For the photograph James T. Kirk examines of the bombing's aftermath, actors were filmed against a bluescreen backdrop, standing very still.