RAF planes have evacuated 301 British nationals or other eligible people from Sudan by lunchtime on Wednesday, No10 said, with eight rescue flights due by the end of the day.
Four UK evacuation flights had taken off since Tuesday with one more loading up at the airfield north of Khartoum at midday on Wednesday.
Britain is also exploring opening up an evacuation route through Port Sudan on the Red Sea.
Warship HMS Lancaster was set to arrive off the coast of Sudan on Wednesday, with RFA Cardigan Bay due to follow.
Deputy Prime Minister Oliver Dowden was due to hold another meeting of Whitehall’s emergency COBRA committee on Wednesday afternoon on the crisis.
Port Sudan on the Red Sea could be used for evacuations if the 72-hour ceasefire between warring factions in Sudan collapses and stops the use of the airfield north of Khartoum for evacuation flights.
It could also later be used to bring in supplies to tackle a feared humanitarian crisis.
A third evacuation flight landed at Cyprus’s Larnaca international airport on Wednesday morning.
Two had already touched down, with the first one carrying around 39 rescued citizens.
Ms Braverman said: "We commenced an evacuation mission in the last 24-48 hours and we expect there to be approximately 200 to 300 people who have been relocated from Sudan in the last few flights.
"We are now commencing an extensive operation, working with over 1,000 personnel from the RAF and the armed forces."
She defended the UK's response, saying the Government had to cope with a "larger cohort of British nationals in Sudan compared to many other countries".
Germany, France and other nations were quicker at extracting their nationals from Sudan.
British troops were due to take over security at the Wadi Saeedna airfield, north of Khartoum, and the evacuations could be stepped up.
Earlier, Cyprus said it had activated a humanitarian rescue mechanism to evacuate third-country civilians through the island from Sudan, following a request from the UK.
A No10 spokesperson said that around 120 British troops were at the Sudan airfield to provide protection but would be made to avoid “active engagement” with other forces.
Border Force and Foreign Office staff were at the site north of Khartoum as UK citizens were going through a makeshift processing centre.
Sudan update: We are evacuating British passport holders and immediate family members with existing UK entry clearance.
— Foreign, Commonwealth & Development Office (@FCDOGovUK) April 25, 2023
🔗 https://t.co/1kt7BdOm2a pic.twitter.com/7fTmW8Z3VZ
The Foreign Office has issued travel advice to trapped Britons eligible for the flights to get to the Wadi Saeedna airfield by their own means.
Appearing before the Commons defence sub-committee on Tuesday, Defence Secretary Ben Wallace emphasised that the 72-hour ceasefire represented a “window” for the evacuation but “it is a volatile situation”.
The possibility of a seaborne evacuation from Port Sudan was also being considered, he said.
“It is a more benign environment, it is an access into the Red Sea and to commercial airports in places like Jeddah (in Saudi Arabia) and gives us space and time in order to process many people there,” Mr Wallace said.
He said Royal Marines were already in Port Sudan to “establish the safety of the area and any options” so “we are in a good position there should we wish to increase support”.
Two warships, HMS Lancaster and the RFA Cardigan Bay, were both going to head to the port, he explained, partly because the evacuation operation may later turn into a wider humanitarian mission for the war-hit country.
As the rescue operation through the Wadi Saeedna airfield was under way, Downing Street said: “We are continuing to operate evacuation flights for as long as possible.”
But the Prime Minister’s official spokesman stressed it was a “fast-moving, complex and dangerous situation” amid the fragile ceasefire between two warring factions.
C130 Hercules and A400 aircraft based at RAF Akrotiri in Cyprus are understood to be taking part in the rescue operation.
The spokesman added: “They will bring British nationals to Cyprus and then they will be able to travel on to the UK, in fact we will be facilitating their travel.”
Rishi Sunak ordered the air evacuation late on Monday night.
Flights areopen to those with British passports and priority is being given to family groups with children and/or the elderly or individuals with medical conditions.
Mr Sunak described the evacuation of British passport holders from Sudan as "large scale".
The Prime Minister tweeted: "The Government has begun a large-scale evacuation of British passport holders from Sudan on RAF flights. Priority will be given to the most vulnerable, including families with children and the elderly.
The Government has begun a large-scale evacuation of British passport holders from Sudan on RAF flights. Priority will be given to the most vulnerable, including families with children and the elderly.
— Rishi Sunak (@RishiSunak) April 25, 2023
I pay tribute to the British Armed Forces, diplomats and Border Force staff…
"I pay tribute to the British Armed Forces, diplomats and Border Force staff carrying out this complex operation. The UK will continue to work to end the bloodshed in Sudan and support a democratic government."
Senior diplomats were overseeing the evacuation effort.
The Foreign Office said it will contact those who are eligible for evacuation directly and British nationals should not make their way to the airfield unless they are called.
The UK government is coordinating an evacuation of British nationals from Sudan.
— James Cleverly🇬🇧 (@JamesCleverly) April 25, 2023
We have started contacting nationals directly and providing routes for departure out of the country.https://t.co/71LU7TgtCC
The UK government has updated its travel advice to highlight these flights.
More than 420 people, including 264 civilians, have been killed and over 3,700 wounded in fighting between the Sudanese armed forces and the powerful paramilitary group known as the Rapid Support Forces as two generals fight for power.
