For this selfless act, he was recently awarded a bronze medal by the Royal Humane Society, a British charity that grants awards for acts of bravery in the saving of human life.
Brandon, who had been preparing for a marathon at the time, was 16km into a 30km training run when he saw a crowd on the bridge staring at a woman in the water.
"I had never run that route before, so it seemed like fate, like maybe I was meant to be there," he recalls. A man asked him if he could help and he had a very short time to make a huge decision – was he going to try and save the woman, or was he going to watch her drown?
Having played competitive water polo for both Paul Roos Gymnasium and Maties in his hometown of Stellenbosch, Brandon is an experienced swimmer with knowledge of water rescue.
"I realised that I was probably her best chance," he said.
It did, however, cross his mind that the waters of the Thames are quite treacherous and that a man had drowned in the exact same spot a few weeks before after attempting a similar rescue.
Nevertheless, Brandon decided to jump. Unfortunately, the place where he entered the water was quite shallow, and he hit submerged rocks not even two meters below the surface, breaking his foot in multiple places, tearing his meniscus as well as his PCL ligament in his knee and suffering severe bone contusions and lacerations on his feet.
Still, he swam to where the woman had last been seen.
"People were pointing to me where she had gone under, and I managed to find her and pull her up. I was so relieved that she was still alive. She was very stressed and shaken and immediately started to struggle. I was expecting that, but it made it very hard."
He managed to swim to the shore, and they were both taken to hospital.
Although he knows the woman survived, he has not heard from her since.
"I also don’t expect to hear from her, but I hope she's well."
Brandon spent 4-5 months on crutches and has been focusing on recovery and rehabilitation ever since. He hopes to be able to complete a half marathon on the anniversary of the rescue.
He described the awards ceremony as a very special event.
"It was a real honour to be there and receive this award from Princess Alexandra. It’s not every day that you get to meet the queen’s cousin. There were some amazing stories of people being selfless and putting their lives at risk to save others. So, I felt it was a great thing to be a part of."
He is often asked whether he would do the same thing again.
"My answer is definitely yes. You can't put a price on someone's life."