BELFAST (Reuters) - Britain on Tuesday rejected an Irish demand for a role in running Northern Ireland if parties there fail to revive a devolved power-sharing government, as unionists said concessions would lead to  grave consequences  for Theresa May s government.  The 1998 peace deal that ended 30 years of violence in Northern Ireland between Irish nationalists and pro-British unionists provides for a consultative role for the Irish government in the running of the British region.  Since January Irish nationalists Sinn Fein and the Democratic Unionist Party (DUP) have failed to reach agreement on re-establishing the devolved administration. The British government has warned it may soon have to step in to rule the province directly for the first time in a decade.  Irish Foreign Minister Simon Coveney on Tuesday told journalists in Belfast that if talks to form a power-sharing government failed  there can be no British-only direct rule,  adding that this was Irish government policy.  He did not say what kind of role he expected for the Irish government and said he was still hopeful devolved power-sharing could be rescued.  In an apparent rebuff to Coveney, a British government spokesman said in a statement that London would  never countenance any arrangement, such as Joint Authority, inconsistent with the principle of consent in the (Good Friday) Agreement.   In the absence of devolved government, it is ultimately for the United Kingdom Government to provide the certainty over delivery of public services and good governance in Northern Ireland, as part of the United Kingdom,  the statement said.  DUP lawmaker Jeffrey Donaldson, whose party Prime Minister Theresa May s minority government depends on to survive, warned that his party would not accept any concessions to Dublin.    Even if we have a temporary period of direct rule, the Irish Government must be clear that it must not interfere with the internal affairs of Northern Ireland and to do so would be a fundamental breach of faith,  Donaldson told the Belfast Telegraph newspaper in comments published on Wednesday.   If that were to happen it would have grave consequences for the stability of the government at Westminster and for the prospect of restoring devolution in Northern Ireland,  he was quoted as saying. 
Britain rejects Irish call for role in Northern Ireland rule