According to Express, one parent by the name of Chloe Koroma spoke with the Duchess of Cambridge - who is assisted by the voluntary home visiting programme Family Nurse Partnership (FNP).
When Koroma's son Oliver presented Kate with flowers at the event, she spoke about Prince George.
"It was lovely meeting the Duchess. She asked how old Oliver is and what football shirt he was wearing," Koroma told the publication.
"She said children grow up so quickly and she can’t believe George is six already."
WATCH: Kate Middleton visits health centre in Camberwell
Kate, who wore navy polka dot blouse with high-waisted wide-leg black trousers to the health centre, attended the event to learn more about the FNP initiative.
The FNP programme at Sunshine House Children and Young People’s Health and Development centre will assist young mothers and pregnant women.
"My nurse Debbie was a fantastic support throughout my pregnancy. She was always there for me and gave me lots of advice and guidance," Koromo told Express of the service.
"I have bipolar and following the pregnancy, I suffered from postnatal depression so I really appreciated her support. I no longer use the service but I’m still in touch with Debbie as she was a big part of my life."