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The scary incident happened at about 2pm on Thursday.
An eyewitness said the men were riding around in a ‘threatening manner’ and trying to steal people’s mobile phones.
Intimidating scenes included one of the bikes mounting a pavement in a bid to snatch a phone out of the hands of a passer by.
And they came close to hitting pedestrians during the bizarre incident outside the BBC’s Broadcasting House.
Their faces were mostly covered by helmets and three of the four men pictured were wearing gloves.
One of the passengers can be seen holding a hammer, and another is wielding a metal bar.
Chief Superintendent Peter Ayling of Westminster borough said: ‘We are working hard to keep the public safe and make the streets hostile territory for criminals who use mopeds, motorbikes and bicycles to snatch valuables from members of the public.
‘We have been made aware of this serious incident and it is a top priority to identify and arrest these reckless offenders who have little regard for their own safety, or the safety of others.
‘A vast majority of offences involving moped enabled snatch are opportunistic and do not involve violence or showing of weapons.
‘It is important that the public are aware of their surroundings at all times and protect their personal property, as this crime happens in an instant. I would urge people to consider using a hands-free device to make a call and do not text or use apps by the roadside, where they are most vulnerable to snatch-theft.