Natasha Sinha, 15, from Greenwich, who was nominated to carry the torch for her dedication to swimming and cross-country running, took the flame down into the equestrian arena.
It was then carried around Cristopher Wren's Naval College before arriving at the Cutty Sark, which has recently undergone a £50 million renovation.
Sir Robin Knox-Johnson, the first person to sail solo non-stop around the world, founder of the Clipper Round the World yacht race in 1995 and a Cutty Sark trustee, ran the torch around the clipper to delighted cheers from the crowds.
The torch later made its way to Jaco Van Gass, 25, from Woolwich, who carried the flame on to the stage at the Woolwich Live Site, a screen which broadcasts local news and BBC coverage of major events, sport, arts and entertainment.
Mr Van Gass lost a leg and part of an arm and suffered severe internal injuries while serving with the First Paras in Afghanistan, but has since walked to the North Pole for charity with other disabled soldiers. He is in training to climb Mount Everest.