The origin of the name "London SS" is disputable. Geir Wade claims to have been the first to propose it:
"Andrew Matheson begs to differ, even though every other band member insists that it was immediately following Geir's arrival that the band's old name, 'The Delinquents', was dropped. Brady confirms it was Geir who came up with the replacement name, but John insists it was the result of a general brainstorming session with a dictionary and thesaurus. Obviously, the London prefix was a nod in the direction of The New York Dolls and The Hollywood Brats."
The group's name caused disquiet in some quarters, because "SS" was generally understood to refer to the Schutzstaffel, an elite paramilitary force of Nazi Germany, some of whose members were convicted of war crimes. This came to haunt Mick Jones when The Clash became Britain's premier left-wing political band. When questioned about the name, Tony James stated:
"We hadn't thought at all about the Nazi implications. It just seemed like a very anarchic, stylish thing to do." 
The London SS recruited Kelvin Cyril Blacklock to front their band. Blacklock's arrival led to Geir Wade and Mick Jones's departures. The band then changed its name to Violent Luck.
"Even while still with Overtown, Kelvin had kept his options open by attending auditions for several other bands. One of the Melody Maker ads he answered had been placed by bassist Tony James. Tony was reading mathematics at Brunel University in Uxbridge, on the western outskirts of London and living in Twickenham, a few miles to the south."
In an effort to soften the blow of Mick's sacking, Blacklock suggested that he team up with the new band, minus James. In Pete Frame's Two Family Trees, the story of The London SS starts with this encounter.
The second lineup of The London SS started with Blacklock and James. The band spent most of their short history auditioning potential members. Besides Blacklock and James, guitarist Brian James (no relation to Tony James) was the only other semi-permanent member at this time. Other musicians who played with them included Matt Dangerfield and Casino Steel, then members of The Hollywood Brats, who would later go on to play in The Boys.
Many other notable musicians tried out for the band but did not make the cut. These included two future members of The Clash, Paul Simonon and Terry Chimes. Another future Clash member, Nicky "Topper" Headon, was asked to join but declined. Rat Scabies, future drummer for The Damned, played with the band even though he was in his own protopunk band, Rot, at the time. Roland Hot also served as drummer. Punk poet Patrik Fitzgerald also claims to have auditioned for the band.
The London SS's only recording was a demo featuring James, Jones, James, and Hot. Musically, they played straightforward rock 'n' roll and covered 1960s R&B. An example of this is their song "1–2 Crush on You", which was later recorded by The Clash.
Brian James left The London SS with Rat Scabies to form The Subterraneans and, later, The Damned. Tony James joined the band Chelsea with Billy Idol and the two later started Generation X. According toChelsea drummer John Towe,
"When Brian James played with London SS he wrote a song called 'Why Won't She Talk' [...] October kept the tune but put new words to the song and re-titled it 'Get Out and Walk'. When he discovered that the tune had been ripped off (early '77) he dropped it from Chelsea's set."
Jones and Simonon teamed up with Joe Strummer and founded The Clash. Ultimately, The London SS members were more famous for what they did later than they were for anything that they accomplished during the band's existence.
In 2012 Brady put together a new lineup, featuring himself along with Jimi McDonald, Taj Sagoo, Michael Kane, and Andi Emm.