The UK's first evacuation flight carrying British nationals has now left Sudan, Downing Street has confirmed.
At least two more flights are expected overnight, as the military attempts to get hundreds out of the war-torn country during a 72-hour ceasefire.
Families with children, the elderly and people with medical conditions will be prioritised on RAF flights leaving from an airfield near the capital Khartoum.
They are being told to make their own way to the airport, without an escort.
No 10 said the situation is "fast-moving" but the first flight is expected to arrive in Cyprus later, before people are transported back to the UK.
At least 459 people have been killed since fighting broke out on 15 April.
A temporary pause in fighting between rival military factions appears to be holding, although there have been reports of new gunfire and shelling, and previous agreements have broken down.
UK ministers have come under increasing pressure to help its citizens flee the fierce fighting.
Around 4,000 UK citizens are thought to be in Sudan and 2,000 of them have already requested help, Foreign Office minister Andrew Mitchell said on Monday.
Only British passport holders and their immediate family with existing UK entry clearance are eligible, the government has said.
The Foreign Office initially said people should not travel to the evacuation site until told to do so - but updated its advice on Tuesday afternoon urging people to make their own way to the Wadi Saeedna airfield to the north of Khartoum "as soon as possible".
The advice published online warned evacuees that "travel within Sudan is conducted at your own risk and plans may change depending on the security situation".
An RAF plane took off from the airfield north of Khartoum and landed in Cyprus earlier on Tuesday afternoon, according to a flight tracking site. It is understood the initial flight was not carrying civilians and was instead focused on security.
Germany, which has been running operations at airfield, is due to end its evacuation later on Tuesday after airlifting around 500 people.
UK defence secretary Ben Wallace told a Commons committee earlier today that 120 British troops were involved and "stand prepared to take over" from the Germans when they leave the site.
He also confirmed that Royal Marines are continuing to prepare an alternative route out of Sudan via a port on the east coast, as well as making contingencies for any humanitarian response.
Foreign Secretary James Cleverly said the government was not able to escort people to the airfield and British nationals would need to "make their own way there".
He said he had made contact with the military leaders in Sudan but it was impossible to predict how long the evacuation window would remain open.
They would maintain the airhead for "as long as we can", he added, and the UK was working as quickly as possible to get people out.
Mr Cleverly said the situation there remained "dangerous, volatile and unpredictable".
"This is an active conflict, the ceasefire has been announced but we know there have been pockets of violence even within previous ceasefires," he added.
One man with dual nationality said he feared he might not make it out of Sudan.
Musaab, who is waiting to be evacuated from Khartoum, told the BBC the situation was fraught with challenges.
"The one thing that I didn't like is that they're asking people to come to the airport which is very risky because there is no law and order," he said.
Many British nationals have spent days indoors with food and drink running low and no electricity or wifi.
Several have spoken of their anger and desperation at being left behind, while other foreign nationals and embassy staff were flown out.
On Sunday, the UK airlifted diplomats and their families out of Sudan in a military operation.
Sir Nicholas Kay, a former UK ambassador to Sudan, said the situation in Khartoum was precarious and the security situation could change rapidly because there was no trust between the two sides in the conflict.
He told BBC Radio 4's Today programme that moving around Khartoum could be challenging because the bridges crossing the Blue and White Nile rivers were being controlled by armed groups.
Hundreds of people have been airlifted from Sudan by other countries, including more than 1,000 people by European Union nations.
Dr Nala Hamza, whose family is trying to get out of Khartoum, said the evacuation was "good news if it came to reality".
She said her family, who live in the centre of the city, had fled their home at dawn to try to get a bus to the north of the country.
"They were hiding in a room at the back of the house away from windows because of the shooting," she told BBC Breakfast.
Dr Hamza said at least 40 out of 55 hospitals were "not functioning at all" and the system "was already struggling before the war".
There was no safe route to get any help and doctors were exhausted, she added.
Dr Atia Abdalla Atia, the general secretary of the Sudan Doctors Union, agreed the situation was "very bad" and they were doing their best to support people.
He told BBC's Today the hospital he was working in has reached maximum capacity and patients were lying down in reception without beds.
Mo, from Reading, said he was "very scared" for his family, who had arrived in Khartoum the day before the violence broke out.
"They were in that area for the first five days, with no electricity, water running out, they were isolated," he said.
"Even getting to this airport that's being looked at to be evacuating Brits from, that in itself is going to be hard to get to."