The warning came after the mineral-rich African country's Constitutional Court this week ruled that President Joseph Kabila, in power since 2001, can stay in office beyond 2016 without being re-elected.
"We are talking to our European colleagues about targeted sanctions against those responsible" for violence and intimidation against the opposition, said Danae Dholakia, Britain's special envoy to Africa's Great Lakes region.
"The position of the United Kingdom is that the people responsible for acts of repression or violence will take responsibility for their actions or decisions," said Dholakia.
Tension has been growing for months in the DRC because of what the opposition alleges are Kabila's efforts to cling on to power despite the constitution barring him from standing again for a third term.
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Today police fired tear gas to disperse thousands of supporters of Katumbi as he appeared in court over the mercenary allegations.
According to his lawyers, Katumbi was assaulted by police as he arrived at the courthouse in the second city of Lubumbashi, but the claims were denied by the regional police chief.
The wealthy owner of the Tout-Puissant Mazembe football club, three-time winners of the African Champions League, Katumbi is accused of hiring several foreign mercenaries, notably Americans, as his private guards.
An AFP reporter at the scene said police fired tear gas and beat the crowd back with truncheons, while security agents inside the courthouse were trying to eject dozens of lawyers who arrived to support Katumbi.
One of the lawyers, Hubert Tshiswaka, told AFP they had come to offer free legal assistance to Katumbi "and all the other people arrested over this inquiry".