Reports suggested four foreign workers had been killed and seven injured along with up to 15 rebels.
But politicians admitted the picture emerging following the incident at the gas complex in the desert was "confusing".
Foreign Office Minister Alistair Burt said: "I am afraid we should be under no illusion that there will be bad and distressing news to follow from this terrorist attack.
"Those who have been working with the families will continue that work of advice and support, though this will take some time.
"We have already increased our consular staffing in Algiers and we are pressing the Algerian authorities to have access to UK nationals at the site so that we can help with repatriation and evacuation."
Shadow Foreign Secretary Douglas Alex-ander said the events were "grave" and "tragic".
Algerian communi-cations minister Mohamed Said Belaid said: "The operation was successful in neutralising a large number of terrorists and freeing a large number of hostages but unfortunately, we are sorry to say, there were deaths and injuries."
A spokesman for the militants said 35 hostages and 15 rebels had been killed during the rescue when Algerian helicopters strafed the site.
Earlier it had been reported that at least two Scots were among the workers taken hostage by a terrorist group, reportedly linked to al Qaeda. One British citizen had already been reported dead and last night a second was confirmed.
Prime Minister David Cameron said the country should be "prepared for the possibility of further bad news".
Mr Cameron spoke after it emerged Britain had not been pre-warned of the military rescue operation despite the Prime Minister asking his opposite number to keep him fully informed.
The Government's emergency Cobra committee met twice yesterday, with Mr Cameron in the chair.
"I will do everything I can to update people about what is a difficult and dangerous and potentially very bad situation," he said.
The depth of the crisis was underlined by the decision to postpone his long-awaited Europe speech despite arrangements being made for him to chair Cobra from the Netherlands tomorrow.
Foreign Secretary William Hague is cutting short a visit to Australia to return to the UK to help deal with the crisis.
Earlier, the Irish Government said one of its nationals – Stephen McFaul, 36, from west Belfast – had been freed and has made contact with his family.
The group that took the workers hostage at the Statoil facility said the attack was in retaliation for French military intervention against al Qaeda-backed rebels in Mali.