Theresa May has insisted her approach to Brexit will deliver a "good" deal for the UK and enable it to make the most of opportunities around the world.
Speaking in South Africa, she told the BBC she was sticking by her "sensible" plans as they both respected the 2016 referendum vote and protected jobs.
While hopeful of an agreement in October, she said it was right to prepare for leaving without a deal.
Earlier, she announced £4bn of extra British support for African economies.
On the first day of a three-day visit to the continent, the prime minister insisted trade deals with countries like South Africa would be a prize for "global Britain" after it leaves the EU next year.
But the BBC's political correspondent Ben Wright said that as she heads to Nigeria and Kenya this week, she knows a very tough autumn of political bargaining awaits her back home.
In an interview with the BBC, Mrs May played down warnings by Chancellor Philip Hammond last week about the risks of a no-deal exit - which he said could have a £80bn negative economic impact.
She said the comments were based on analysis first released in January that were, at the time, a "work in progress".
Mrs May then cited comments by the head of the World Trade Organisation, who said Brexit "won't be a walk in the park, but won't be end of the world either".
"We are working for a good deal, we have put forward our proposal for a good deal," she said. "I believe that deal is to the benefit, not only of the UK, but the EU.
"What the government is doing is putting in place the preparations to make sure we can make a success whatever our future relationship is with the EU and whatever the outcome of the negotiations."
By the BBC's Ben Wright in Cape Town
With dogged determination Theresa May danced along with a group of children in a soggy Cape Town playground - her first stop on a three-day dash around sub-Saharan Africa.
It is the first No 10-led business delegation to Africa since 2011. The school children symbolised, she said later, the dynamism and creativity of the continent's growing and youthful population.
And it is jobs for these young people and millions like them that the UK wants to help African economies create - using UK companies, capital and government help to invest in African countries in the hope of keeping them politically stable later on.
At a speech in the city on Tuesday, the prime minister pledged an extra £4bn in direct UK government investment - which she expects to be matched by the private sector.
Mrs May also said the UK would fundamentally shift the way it spends aid money - to focus on long-term economic and security challenges rather than short-term poverty reduction.
For the UK of course, Brexit is a spur to expand trade beyond the EU, which is by far our biggest market.
Some Tory MPs have said they cannot support Mrs May's blueprint for the UK's future relations with the EU, saying it is a betrayal of the millions who voted to leave the EU in 2016.
But Mrs May said the proposals were sensible as they insisted that an end to EU freedom of movement and the jurisdiction of the European Court was "non-negotiable", while ensuring British manufacturers had unrestricted access to an EU wide free trade zone for goods.
"It is right as we look to our future relationships that we protect jobs and livelihoods," she added.
As part of a renewed focus on Africa, Mrs May has said she wants the UK to become the continent leading's investment partner within the G7, overtaking the US.
She told the BBC that this was not unrealistic, given that the UK was already the largest foreign investor in South Africa, the continent's largest economy.
"One of the benefits of leaving the EU is that we will be able to negotiate our own trade deals in the future," she said.
"We look to a global Britain outside the EU making the most of those trade deals around the rest of the world."