Britain acted after claims Rwanda is funding the rebel army which is causing bloodshed across the border in the Democratic Republic of Congo
A rebel army, called M23, seized the provincial capital a week ago, defeating the hapless Congolese army.
Thousands of civilians have been forced to flee as M23 rebels in the Congo consolidated their position in Goma.
The UK has announced it is withholding £21 million of aid to Rwanda, due next month.
The UK says it is concerned it is supporting rebels in the DRC. Consecutive UK Prime Ministers have praised Rwanda's leadership.
Britain will withhold £21 million of aid to Rwanda amid concerns that the state is supporting rebels in the Democratic Republic of Congo (DRC).
International Development Secretary Justine Greening said the money was being withheld due to "creditable and compelling reports" President Paul Kagame had breeched aid agreements.
The Government has already set out its concerns over credible and compelling reports of Rwandan involvement with M23 in DRC. This evidence constitutes a breach of the partnership principles set out in the Memorandum of Understanding and, as a result, I have decided not to release the next payment of budget support to Rwanda.
International Development Secretary Justine Greening said that the UK was withholding £21 million of aid due to be paid to Rwanda next month.
Rebels in Democratic Republic of Congo have said today that they will withdraw from the city of Goma only if President Joseph Kabila agrees to their demands, which the government was quick to dismiss as a farce.
The deadlock raises the risk that the insurgency may turn into an all out war in a region affected by almost twenty years of conflict.
Rebels in the Democratic Republic of Congo (DRC) are set to withdraw from the eastern cities of Goma and Sake following negotiations in Uganda.
Colonel Sultani Makenga, the leader of the M23 group, is said to have accepted the demand without conditions.
Uganda's chief of defence forces, Aronda Nyakayirima, told Reuters: “We met last night and I communicated to him [Makenga] the decision of regional leaders reached on Saturday and he accepted to pull back his forces out of Goma and Sake and also stop any further advances southward.
"He didn't put up any conditions for pulling out because he agreed that all their grievances will be resolved in the ICGLR [Great Lakes] mechanism as stipulated in the declarations of the Saturday summit [in Kampala]."
African leaders urged the M23 on Saturday to end their aim of toppling the DRC government.
2012: The city of Goma is captured by troops from the rebel group M23, which is backed by Rwanda and Uganda, according to the UN.
2005 - 2011: Mutinies by soldiers claiming lack of pay and poor conditions, ongoing clashes between the Congolese army and FDLR rebels, occupation by Joseph Kony's LRA in the east, UN accusations of war crimes and mass rapes.
2003 - 2005: Under an interim government lead by President Kabila, the country sees repeated coup attempts, the arrival of UN troops, and fighting between rebel groups and soldiers in the east.
1998 - 2003: The second Congo war, fought at times between seven nations and many more militia groups, is said to be the deadliest since World War II.
In 2001 Joseph Kabila succeeded his father, who was shot dead by a bodyguard, as president.
1996 - 1997: The first Congo war, sparked by destabilisation caused by refugees from the Rwandan genocide, results in Laurent Kabila becoming president and renaming the country from Zaire.
An M23 chief tells me they'll ignore demands to leave Goma by 12pm.
He says he wants to talk, not fight: "We cannot sacrifice a million brothers," he said.