RNA - The incident being investigated happened on Oxford Street on 14 April and was filmed by human rights campaigners Isa al-Ali and Moosa Abdali, Middle East Eye reported.
The police have also received a complaint about alleged "malicious communications" sent through social media to the activists in the hours following the altercation on Oxford Street.
The investigation comes amid a continuing rights crackdown in the kingdom. Bahraini police raids left five dead in late May in some of the worst violence seen in the country since 2011.
The case also threatens to embarrass the British royal family. MEE understands the police investigation was launched just days before the Queen rolled out the red carpet for the King of Bahrain Hamad al-Khalifa at the prestigious Royal Windsor Horse Show last month.
Bahraini activists, including some of those whose claims are at the center of the investigation, disrupted the show in 2013. Rights groups now fear that Bahrain has extended its ongoing crackdown to the UK in an attempt to stifle further protest.
The video of the altercation on 14 April appears to show Khalid bin Ahmad al-Khalifa. The video also appears to show Rashid, an officer in Bahrain's military, making threats against Abdali, 36, and al-Ali, 22, including what seems to be a veiled threat against the men's families in Bahrain.
Dissidents Ali and Abdali have also complained to the police in London that they and their families received several threats on social media after the altercation on Oxford Street.
Human Rights Watch, which investigated the incident, said one message sent to Ali from the social media account of Khalid bin Ahmad Al Khalifa said those involved in the altercation on Oxford Street would "bear the consequences... from me personally".
The altercation came weeks before the Windsor Horse Show, which is a key event in the British and Bahraini royal families' summer schedules.
The event saw Bahrain's ruler sit alongside the British queen in a "Kingdom of Bahrain Lounge". Former British Prime Minister David Cameron, who visited Bahrain in January, also attended.
Campaigners say the Windsor event also coincided with the detention in Bahrain of several family members of UK-based activists in what they suspect to be an attempt to stifle protest at the event.
The weekend of the event also saw firebomb attacks on vehicles owned by opposition figures in Bahrain, they alleged.
Bahrain, which hosts a major US naval base and a smaller British naval facility, has been plagued by sectarian tensions since the 2011 Arab uprisings.
The ruling family has responded by stifling dissent, banning the main opposition group, al-Wefaq, and revoking the nationality of Bahrain's opposition leader cleric Isa Qassim.
On 31 May, Amnesty International warned that the country was heading for the "total suppression" of human rights after the secular National Democratic Action Society (Waad) was banned by authorities.
Abdali and Ali both fled Bahrain and sought asylum in the UK, Abdali in 2007 and Ali in 2014 - after claiming they were tortured by security forces.
At the time, Ali claimed he was arrested in February 2013 after taking part in anti-government protests. He said he was beaten and that a knife was held against his groin by a police officer. He was released on bail but received death threats before he was able to exit the country and come to the UK via Dubai.
HRW has also documented comments from the social media accounts of Rashid al-Khalifa and Khalid bin Ahmad al-Khalifa appearing to welcome firearms attacks on the hometowns of Adbali and al-Ali in Bahrain.
The posting from the account of Khalid bin Ahmad al-Khalifa states: "This is the fate of anyone who attacks, even with a single word, the strike was near the house of the effeminate terrorist Moosa Abdali and the next will be worse, God willing, I told you in London, go, go and you will see something you can't believe."
The police investigation in London also comes as the British government is facing renewed criticism over its £2m ($2.6m) programme of "technical assistance" for Bahrain's security and justice system.
The security and aid programme is partly funded by the controversial Conflict, Stability and Security Fund. Last month the Guardian reported that the fund was used to pay for a Royal Marine Band to play in Bahrain for the Queen's 90th birthday celebrations in 2016.
MEE can also reveal that the police probe has the potential to doubly embarrass the British government. Khalid bin Ahmad al-Khalifa was in the UK on 13 April, the day before the events under police investigation, to attend the Sovereign's Parade at the Sandhurst Royal Military Academy. His son Rashid was one of the graduates addressed by Prime Minister Theresa May.
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