The youth centre is named in memory of 10-year-old Damilola Taylor, who died from a stab wound in November 2000.
Southwark Youth Service has now stepped up its ongoing staff consultation programme so full- and part-time youth workers can air their views on safety and security at the centre.
The stabbing happened in the day during a project session run in partnership with Southwark Council's social inclusion unit. Two tutors were in the class and another two youth workers were on duty at the time.
The 17-year-old was taken to hospital where he is said to be "in a serious condition but fine" following the incident on 4 February. A 14-year-old male, who was unknown to staff and "not meant to be in the centre", was accused of assault the following day. He was remanded on conditional bail on 5 February.
Tracy Browne, former Damilola Centre manager and area youth development worker for Peckham and Nunhead, said: "We're all shocked at this one-off event after all the work we've done in improving the centre."
She added: "The centre operates a zero-tolerance approach to weapons, drugs and swearing. We don't want to overreact by saying we have to search all young people coming into the club with metal detectors."
Karl Murray, head of Southwark's youth and Connexions service, said: "We know (the young people) will be feeling vulnerable now but it's hoped our support sessions with them will put their minds at rest."
The centre, which was closed to young people from 4 February to 9 February, was refurbished in 2001 after the murder of Damilola Taylor.