The government insists it is in touch with Britons still stuck in Sudan after an evacuation operation only rescued diplomats and their families.
Minister Andrew Mitchell said 2,000 UK nationals had registered for help, but there could be up to 4,000 in Sudan.
The British diplomats, flown out on Sunday, had been in a terrible position surrounded by fighting, he added.
Violence in Sudan between two opposing forces has seen deadly shooting and shelling in the capital, Khartoum.
Foreign Secretary James Cleverly has warned help for Britons will remain “limited” until a ceasefire is reached – as some said they felt abandoned by the UK government.
Alicia Kearns, conservative MP and chair of the foreign affairs select committee, said the lack of contact with British nationals in Sudan “would suggest that no lessons have been learnt since Afghanistan”.
The power struggle that erupted last week between Sudan’s regular army and a paramilitary force called the Rapid Support Forces (RSF) has also affected other parts of the country, leading to a growing humanitarian crisis.
Electricity is scarce, and food and water supplies are running out for many.
Sam, a British businessman living in Sudan, told the BBC that news of the UK evacuation at the weekend “gave us hope, but in the absence of any information from the government this was clearly a solution for diplomats only”.
He described the situation as a “nightmare for those of us left behind”, and said he knew of many people from other countries such as Hungary and South Africa whose embassies were making plans to evacuate nationals.
Speaking to the BBC, Mr Mitchell said British Embassy staff had been between the lines of fighting and in “very great danger” – with one official held at gun point.
Over the weekend, the prime minister confirmed that British diplomats and their families had been evacuated in a “complex and rapid” operation.
It is understood that UK special troops landed in Khartoum with a United States evacuation team on Saturday.
Military vehicles were then used to collect UK embassy staff and their families, before they were airlifted to Cyprus on Sunday morning in a convoy of RAF aircraft.
The government has a “specific duty of care” to diplomats evacuated from Sudan, Mr Mitchell told BBC Radio 4’s Today programme.
He also said a civilian evacuation had not possible on Sunday, but “we are exploring every possible opportunity to get our citizens out”.
The minister called for a ceasefire in Sudan, and urged Britons to follow government advice to “stay indoors”.
UK citizens in Sudan are being asked to tell the Foreign Office where they are in case more help becomes available, and a hotline has been set up for those who need urgent help.
Mr Mitchell said about 2,000 people had registered for assistance with the foreign office, with the figure rising over the last two days.
He insisted that electronic messages from the foreign office emergency team were being sent every day, but explained they might not always arrive.
Defence Secretary Ben Wallace told BBC News the British army, Royal Navy and the Royal Air Force had been involved in the weekend rescue, with C-130 Hercules and Airbus A400M transport aircraft used.
Another UK citizen in Sudan, William, described a chaotic situation as he opted to leave Khartoum on a bus organised by his Sudanese employer, to take him and other nationals to Egypt.
Speaking to the BBC’s Newshour programme, he said the UK government had given him “nothing” in terms of support, adding: “We had to basically go private, we’ve had absolutely nothing but nonsense from the government, and not even nonsense. We’ve had nothing.”
William described waiting to be collected by the bus as a “dicey situation” with “gunfire going off all the time”.
Ms Kearns said evacuations were proving enormously difficult “but we have to get our people out”.
Asked on the Today programme about a person who claimed they had only received two text messages from the government, Ms Kearns said: “So that would suggest that no lessons have been learned since Afghanistan, and I have urged the government to make sure they are communicating regularly with British nationals.”
However, Downing Street said “significant lessons” had been learned from the evacuation of Afghanistan in the face of the Taliban’s takeover.
The prime minister’s spokesperson said the government would “pull every leaver possible” to help Britons in Sudan and to bring about a ceasefire.
Mr Sunak and Egyptian President Abdel Fattah al-Sisi agreed on Sunday that the UK and Egypt would work with international partners on diplomatic efforts to secure a ceasefire.
A further Cobra meeting – an emergency response committee made up of ministers, civil servants and others – to discuss Sudan’s “escalation” of violence, is expected later.
Several other countries including the US, France, Germany, Italy and Spain have been evacuating their diplomats and citizens.
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