Britons in the Democratic Republic of Congo's South Kivu should leave, the Foreign Office has strongly advised, as rebels plan to seize the local capital.
Rebels from the M23 movement have already taken Goma, in North Kivu, and have said they will head to Bukavu, 230km (143 miles) to the south.
The FCO said a British embassy official was available to help Britons at the border crossing into Cyangugu, Rwanda.
Many foreign groups are planning to leave on Thursday, it said.
The Foreign Office's updated travel advice said: "If you choose to remain in Goma or Bukavu against our clear advice, you should be aware that our ability to provide consular assistance will be extremely limited.
"As such you should be prepared to move quickly (including having up-to-date travel documentation) or stay in a safe place for a period of time."
It said the overall level of the advice had not changed, and it still advised against all travel to eastern and north-eastern DRC, and all but essential travel to the rest of the country.
The rebels, who say they are ready to topple President Joseph Kabila, entered Goma on Tuesday, skirting around a UN compound as Congolese army forces retreated.
France has heavily criticised the failure of the UN force, which has about 19,000 troops, to stop the rebels.
UN officials said its troops had fired hundreds of rockets in an effort to block the rebel advance on Goma, but that they wanted to avoid triggering a battle in Goma, and that they were limited by their mandate.