Northern Ireland will get no extra money to fill a £750million hole in its welfare benefits bill because it has refused to follow cuts imposed by the British government, prime minister David Cameron has insisted.

The position was spelled out during a meeting today at Westminster with Northern Ireland First Minster Peter Robinson and Deputy First Minister Martin McGuinness.

Later, Mr Robinson and Mr McGuinness clashed over the issue, with Mr Robinson saying it was an “outrage” that Sinn Féin would not agree to welfare changes, arguing that cuts in health and education were being made to fill the gap.

Northern Ireland will not have to implement the unpopular “bedroom tax” under which social housing tenants lose benefits if they have spare bedrooms. But the British government insists that it must apply the £25,000-a-year cap introduced last year on what a person can receive in certain benefits as well as make cuts to incapacity benefits and changes to tax credits.

“We have to recognise that this is as good as it is going to get. The prime minister made it very clear that there was no further flexibility, no further room to manoeuvre. If we want to do anything, then we are going to have to pay for that ourselves,” Mr Robinson said.

The North will face a £200 million funding gap unless Sinn Féin backed down, he said.

“Northern Ireland simply cannot afford Sinn Féin cuts. It is essential that decisions are taken, difficult though they are. If we fail, then we are going to punish vulnerable people in society by cutting the health service, housing, or education.”

Mr McGuinness sought to emphasise that Sinn Féin’s complaint was directed at the British government, rather than the Democratic Unionist Party.

Northern Ireland Secretary of State Theresa Villiers, who attended both meetings, insisted that there will be no concessions from London. “There is no scope for negotiations. The package was adopted to Northern Ireland’s special circumstances. That is as far as it goes. If the Northern Ireland Executive wants to run a different welfare system, that is open to them under devolution but they must meet the cost of that themselves.”