Their work references brands such as Nike, Footlocker, JD Sports, McDonald's and Locog.
The group has dubbed the campaign 'Brandalism' and claims to have installed 35 anti-advertising artworks across Leeds, Manchester, Birmingham, Bristol and the capital.
Outdoor media owners JCDecaux, Primesight and Clear Channel have begun removing the group's work from their affected sites.
Baker said: "We want to squash it as quickly as possible and return to normal", adding that the OMC took the activity very seriously and was prepared to issue a cease-and-desist order.
However, Baker is keen to speak to the Brandalism group directly before any definitive legal action is taken.
Baker told ±±¾©Èü³µpk10 that graffiti on billboards is not a new idea, but that the OMC and media agencies involved would get the billboards changed as quickly as possible in order to give the campaign "minimum publicity".
He called the activity no different to fly-posting and described the work as "spurious".
He said: "Nike is a brand sometimes associated with ambushing. Now they have ambushed the ambusher, which seems spurious."
The Advertising Standards Authority (ASA) said the case was outside its remit as it was an illegal activity.
A source close to Nike said: "Nike is aware of the activity, but it does not want to give this organisation the oxygen of publicity, so will not be contacting the police about it."
The OMC issued the following statement:
"The outdoor industry deplores this irresponsible development, being the misuse of poster sites for illegal agitprop messages by 'Brandalism'. We take this criminal activity very seriously and are taking legal advice.
"We want to give the perpetrators the minimum amount of publicity and have mobilised the media owners' operations teams to check all their inventory in the five affected cities. Typically, companies are responding and overposting affected sites within 24 hours. Spares are routinely provided to media owners to cover just these eventualities.
"As with graffiti and flyposting, we will always protect the advertiser's interests as forcefully as we can, and we have taken vandals to court in the past. The scale of vandalism, such as damaged bus shelters, is very low in the UK compared to other countries.
"Advertisers on billboards in the public space are very responsible because ads are seen by all. They are less controversial than in some other media. We have tightened our charter relating to the display of alcohol and sexualised imagery in sensitive locations.
"There are 10,000 fewer billboards than there were 10 years ago – very few inactive boards in out-of-the-way places, in keeping with urban beautification programmes. We think the stated objections to advertising are a misguided and fabricated pretext for what Brandalism see as guerrilla art.
"The UK public has a positive attitude towards outdoor advertising, and complaints are down 40% year on year according to the ASA.
"Most people appreciate that outdoor advertising keeps them informed and subsidises public transport and amenities – they do not see it as a blight.
"The voice of the consumer can be heard in new consumer vox pops being added to the OMC site later today. It is uniformly positive.
"We will continue to monitor the situation and safeguard advertisers' interests going forward. Advertisers should be reassured that we take this situation very seriously and are actively protecting their commercial interests."
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