Andrew Dinsmore was confronted by the robber, who jumped off the back of a scooter and shouted “give me your f****** watch” while waving the knife in his face.
Footage of the robbery shows two males on a scooter, wearing helmets and balaclavas, screeching up to them.
After they grabbed Mr Dinsmore’s watch, his partner collapsed in shock fearing the couple had been attacked by a terrorist and the footage shows her desperately calling for help.
Mr Dinsmore, 32, told the Standard: “We had just had dinner and were walking along in broad daylight. The moped rode up to us and one of them pulled a machete from his tracksuit.
“He threatened me with it and kept saying ‘give me the f****** watch’. “I let him have it. It had great sentimental value but I feared for my life.
“My fiancée thought it was some kind of terror attack, it was frightening. They were targeting the watch I’m sure. The only other thing they took was a bag carrying a pair of new shoes. They didn’t take our phones or my fiancée’s jewellery or anything like that.”
The 30-second video clip shows the robbers racing off before Mr Dinsmore alerted police and armed officers were scrambled to the scene.
They searched for the robbers but no arrests have been made.
Mr Dinsmore, who in the same week as the robbery was elected as a Conservative councillor in Hammersmith and Fulham, said the attack had left him fearing for his safety.
He said: “When I hear a moped near me my adrenaline starts to rush. It’s made me think I can’t even wear a watch when I go out. It’s just not right that these gangs can operate and make us change the way we live.”
He called for a change in the law to stop the sale of machetes and other weapons online.
“I did some research and found that I could easily buy a machete online and as part of the purchase the website suggested that a tomahawk axe and a balaclava were flagged as other purchases often made with the machete. It’s outrageous. There needs to be more regulation.”
His calls have been backed by Chelsea and Fulham MP and Business Minister Greg Hands.
He said: “I was shocked to see my constituent held up in Chelsea in broad daylight. Speaking to Andrew about it afterwards, it is shockingly apparent how easy it is to buy machetes online. I am speaking to the Crime and Policing Minister to see what new laws can be brought in to curb the sale of these weapons.”
Detectives are investigating the incident and appealing for information.
Witnesses are asked to call police on 101 or, to remain anonymous, Crimestoppers on 0800 555 111.