The black Lamborghini Huracan Spyder was rented from Swiss Luxury Car Rental business Scheiwiller in Zurich on Friday by a woman in her late 40s with an Irish identity card, the company say.
She claimed to be driving it to Strasbourg for a meeting then back to Zurich but the car was later tracked driving from Switzerland to London via Dover.
On Sunday the supercar, which has a top speed of 201mph, was seen on Park Lane before it mysteriously disappeared.
At 5pm on Sunday the Scheiwiller's GPS tracker showed it parked at an IKEA car park in Tottenham, north London after the marathon journey.
ID card the alleged thief used to rent the car
Managing director Adriano Scheiwiller said: "She looked well-groomed and had luggage, she said she wanted to attend a meeting in Strasbourg.
"Instead of returning she headed for London, the GPS had betrayed her, she showed how she was shipping the car to Calais and transported it to England.
"It has already been spotted in London."
He added: "It is a big loss and I hope the insurance company will pay out. The British police have done nothing yet, the phone for this woman no longer works.
"We are offering 5,000 Swiss francs to whomever finds the vehicle, it's a big loss."
Before the car allegedly went missing the driver left a deposit of 2,500 Swiss francs - around £2,000 - and the identity card.
Scheiwiller, who believe the ID card shown by the driver was fake, are now offering around 5,000 Swiss francs - roughly £4,000 - to anyone who can find the supercar.
Adriano has reported the theft to the Metropolitan Police.