The police said a warrant was issued against Assange in 2012 after he failed to hand himself in for extradition to Sweden, adding: "The Metropolitan Police Service is obliged to execute that warrant should he leave the embassy".
The Crown Prosecution Service said that breach of bail is punishable by up to a year in prison or a fine.
The police statement said Assange was previously wanted for "an extremely serious offence" in Sweden and the police presence around the embassy had "reflected the serious nature of that crime".
"Now that the situation has changed and the Swedish authorities have discontinued their investigation into that matter. Mr Assange remains wanted for a much less serious offence," it said.
"The MPS will provide a level of resourcing which is proportionate to that offence," it added.
The police ended their round-the-clock guard outside the embassy in October 2015 but said they were strengthening a "covert plan" to prevent his departure.
Assange has been granted asylum by Ecuador and has been able to evade justice because he is on Ecuador's sovereign territory by being in the embassy.
The policing outside the embassy has cost millions of pounds, the source of much criticism in Britain.
"Like all public services, MPS resources are finite. With so many different criminal, and other, threats to the city it protects, the current deployment of officers is no longer believed proportionate," the police said at the time.