They seemed like any other well-off young London couple dining out last Wednesday. The man and woman, both smartly dressed, arrived for their booked table for two at the Michelin-starred restaurant L'Autre Pied in Marylebone, before each ordering three courses from the menu, along with a bottle of pink Larmandier champagne at £124 and another of 1997 Bollinger that cost £285.

But after helping them on with their coats to nip outside for a cigarette, the waiting staff soon discovered that they were no ordinary diners. Some minutes later, with a plum tart and millefeuille uneaten at the table, it became clear the couple had no intention of returning – or of paying a bill totalling £572.74.

What may make the case more intriguing is that the name in which the pair booked the table, Lupin, echoes that of the fictional Arsene Lupin – a stylish Gallic gentleman thief whose adversaries, in a series of novels by Maurice LeBlanc, are invariably portrayed as rather worse villains than him. The Metropolitan police confirmed they were investigating.

"In two decades we have never had anything like this," Leonora Popaj, the restaurant's general manager, told the Guardian. The couple had not seemed unusual or suspicious, she said, and the bill was not particularly lavish by the restaurant's standards – the Bollinger is not, for instance, the most expensive champagne on the menu. "They looked like a very genuine, very lovely couple. Their bill was an average spend. Nothing was out of place or unusual."

CCTV footage of the pair, indeed, showed nothing peculiar: both are believed to be in their 30s; the man, described by the restaurant as about 6ft tall, had a light beard and was wearing blue jeans and a jumper; his companion, wearing a black sleeveless dress with a scarf, had long dark hair and is seen in the snatched image flashing an engaging smile at a staff-member.

It was only while viewing the footage, said Popaj, that she noticed the woman wasn't carrying a handbag – not in itself damning, perhaps, but which certainly facilitated their speedy departure.

It is understood that similar incidents involving other top restaurants are being looked at by police, raising the possibility that the pair are serial thieves. But Popaj denied suggestions that L'Autre Pied will now demand that diners wishing to step outside for a cigarette surrender their credit cards. "We are totally against that. That would only punish our very honest clientele."

As for the suggestion that "Lupin" may have been chosen as some kind of joke, Popaj said: "It makes me very angry. What upsets me most is that they have this mentality that this [amount] is nothing for this level of restaurant.

"They are forgetting that they are really attacking the waiters, who don't have an enormous income."