Personal trainer Victoria Milligan, 45, is unable to work or exercise after her running blade was taken, alongside two other prosthetics.
In total, they are worth around £30,000.
Victoria lost a leg in speedboat accident in Cornwall in 2013, which killed her husband and daughter.
She said: "I want to appeal to the thieves - I really need to get my legs back.
"They're of no use to them whatsoever and have no resale value.
"They would have opened the bag up and had the shock of their lives - I just hope they dump them somewhere.
"They're not going to fit anyone else, they're very expensive but are totally useless to anyone but me.
"I can't really work or exercise, I've got my everyday leg but it's nothing compared to my blade," she added.
In a tweet, she urged members of the public to keep their eyes open for the prosthetics, in case they see them discarded.
According to police, two men on scooters smashed both of the parked car's passenger side windows before stealing two bags from the back seat.
As well as the prosthetic legs, which were inside one of the bags, the thieves also made off with a laptop, which was in the other bag.
Mrs Milligan was in a nearby restaurant when the incident took place between 2.30pm and 4.30pm in Michael Road in Fulham.
Upon returning to her car, she alerted the police.
"This is a heinous crime where heartless thieves have stolen the victim’s personal property, including her prosthetic legs" said inspector Darren Desa, of Hammersmith and Fulham borough.
"This is extremely distressing for the victim.
"We would appeal for any witnesses or anyone with information to contact us as soon as possible.
"I would also appeal to anyone who knows where the prosthetic legs are to do the right thing and hand them in to police or inform police where they are. They are of no use to anyone but the victim," Insp Desa added.
According to police, no arrests have been made in connection with the theft and enquiries continue.
Anyone with information relating to the incident should call police on 101 or Tweet @MetCC.
Alternatively, those wishing to pass on information can do so anonymously by calling Crimestoppers on 0800 555 111 or visiting their website .
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