It comes as the defence secretary is facing a Ministry of Defence inquiry into his working relationship with Mr Werritty, who has no official role.
Prime Minister David Cameron has asked for the preliminary findings to be given to him on Monday.
Labour is demanding Mr Fox makes a full statement in the House of Commons.
According to the Observer, the video images show Mr Werritty at a meeting Mr Fox had with Sri Lankan president Mahinda Rajapaksa in a London hotel last year.
The MoD said the meeting had been a private one and no special advisers had been in attendance.
Mr Werritty, 34, also used to carry business cards which said he was an adviser to Mr Fox, despite having no official capacity within the MoD or the Conservative Party.
The defence secretary Mr Fox has previously said in a parliamentary answer: "Mr Werritty is not an employee of the MoD and has, therefore, not travelled with me on any official visit."
He has since responded to the controversy by saying he has "absolutely no fear of complete transparency in these matters".
He told the Sunday Telegraph: "I think there are underlying issues behind these claims and the motivation is deeply suspect."
Mr Fox ordered the MoD inquiry into whether his working relationship with Mr Werritty, a former flatmate and his best man in 2005, had breached the ministerial code or security.
Then on Saturday, Mr Cameron said he wanted the cabinet secretary to examine the report and he wanted the initial findings on his desk on Monday.
The ministerial code requires ministers to ensure there is no conflict between their public duties and private interests.
Mr Werritty is said to have brokered a meeting with businessmen in Dubai as Mr Fox was returning from a visit to British troops in Afghanistan in June.
The defence secretary and the businessmen reportedly discussed technology that allows service personnel to make encrypted phone calls home.
Mr Fox, who was in Libya on Saturday for talks with the new regime, said defence industry representatives had asked for the meeting in Dubai "when they happened to be sitting at a nearby table in a restaurant".
However, later on Saturday, email correspondence seen by the Guardian appeared to call into question Mr Fox's version of events by suggesting there had been a certain amount of planning to get the meeting organised.
It prompted a spokesman for Mr Fox to clarify that the MP had been referring to Mr Werritty and not himself having been at the impromptu restaurant meeting.
Shadow defence secretary Jim Murphy responded by saying "fresh questions" had been raised about the working links between Mr Fox and Mr Werritty.
"This issue has gone from being embarrassing to being controversial and has now moved way beyond that. This will cause alarm bells to start ringing even more loudly in Downing Street," Mr Murphy said.
He added: "The secretary of state's version of events appear to be unravelling and he now has even bigger questions to answer."
The MoD said that Mr Werritty "never has been part of Dr Fox's official travelling party when the secretary of state is abroad on official business".
A spokesman said: "Mr Werritty's meetings with the secretary of state at the MoD have concerned entirely private matters, not to discuss MoD business.
"At no time has he had access to any classified MoD documents or information."