Algeria operation: UK hostages 'freed'
A Northern Irish man is free reportedly along with two Scots after they were among a group held captive by militants at a gas facility in eastern Algeria.
An Algerian military operation is ongoing. The facility's part operator, BP, says the situation remains unclear.
No 10 says David Cameron was not informed of the operation in advance and only learned of it when he phoned his Algerian counterpart at 11:00 GMT.
A Briton and Algerian died on Wednesday after kidnappers entered the plant.
BBC political correspondent Robin Brant said Number 10 was using diplomatic language but there was no doubt the prime minister was very angry.
"He knows questions will be asked what influence he had trying to secure the release and safety of those [Britons] involved."
As a result of the situation, the prime minister has postponed his long-awaited speech on Europe in the Hague on Friday.
A Downing Street spokesman said: "The prime minister is extremely concerned. It is a very grave and serious situation."
Mr Cameron chaired two meetings of the government's emergency committee Cobra on Thursday, and will chair another on Friday morning.
'Escaped or liberated'
Militants had earlier said they were holding 41 foreign nationals. They were believed to include British, Japanese, US and Norwegian citizens.
BP says there are unconfirmed reports of casualties and of hostages being released or escaping.
The family of 36-year-old Stephen McFaul, from west Belfast, told the BBC he had been freed and was safe.
Another hostage is also reportedly from Northern Ireland. The MP, Ian Paisley jnr, says he was called to the Foreign Office for a briefing about a constituent, a man from north Antrim who was travelling on a British passport.
Meanwhile, the Algerian state media says that some hostages have escaped or been liberated, including two from Scotland, one from France and one from Kenya.
It quoted an unnamed source as saying that "about half" the foreign hostages had been freed.
Media reports quote militants saying 34 hostages and 14 kidnappers were killed after Algerian forces opened fire from the air.
The BBC's security correspondent Frank Gardner tweeted the situation was still very confused "with lots of rumours".
As well as Britons, the hostages are said to include Japanese, US, French and Norwegian nationals.
In a statement, BP's Chief Executive Bob Dudley said: "Supporting these families is our priority and we are doing all we can to help during this sad and uncertain time."
The company added that, as a precautionary measure, staged plans were under way to bring a group of non-essential workers out of Algeria.
The complex at In Amenas is operated by state oil company, Sonatrach, along with Britain's BP and Norway's Statoil.
Algerian Interior Minister Daho Ould Kabila earlier said the militants claimed they had seized 41 foreign workers.
He said the kidnappers were Algerian and operating under orders from Mokhtar Belmokhtar, a senior commander in al-Qaeda in the Islamic Maghreb (AQIM) until late last year, when he set up his own armed group after apparently falling out with other leaders.