The bus was heading into Lydenburg, a town 175 miles east of Johannesburg, when it overturned, said Lydenburg police Inspector Gerrit Smit.
Of the dead, 26 were Britons and one was their South African tour guide, District Health Manager Kathy Olivier said. The driver was among the injured.
The carnage prompted officials to call for tightening transport laws.
In six days, 60 people have been killed and almost 200 injured in four separate bus accidents, creating problems for the country's tourism promotion.
Monday's crash was the only one involving foreigners. It was also the most deadly.
The driver, who escaped with minor injuries, told police the brakes failed as the bus was traveling down a mountain road near the town of Lydenburg, east of Johannesburg. The bus careened off the road and rolled, shearing off the roof as the occupants tumbled out.
Rescue personnel from Lydenburg, which has just one ambulance, were overwhelmed.
"We found a body lying there and a head lying there," a paramedic identified only as Jerry told a TV reporter.
More ambulances were brought in from other towns. They ferried the injured to Lydenburg Hospital.
President Thabo Mbeki said through his spokesman that he was saddened that the victims were visitors who were contributing to the country's tourism industry, which was necessary to improve the economy and create jobs.
"The deaths are not only a loss to the people of Great Britain, but South Africa has lost valuable ambassadors ... promoting the country as a tourist destination," said spokesman Parks Mankahlana.
The bus company, Cape Town-based Springbok Atlas, issued a terse statement saying the cause of the crash was unknown and that the bus had been bound for Pretoria, the capital.
In London, Thomas Cook Holidays said the tragedy happened on day 14 of a 17-day trip, while the tourists were traveling from the exclusive Sabi Sabi game park, which borders Kruger National Park, one of the country's top tourist attractions.
The opposition United Democratic Movement said the crash was likely to harm South Africa's tourism industry, one of the country's top money-makers, which is already threatened by a crime wave.
Transport Minister Dullah Omar planned to meet Thursday with representatives of bus companies amid the mounting body count from bus crashes.
Jeremy Cronin, chairman of Parliament's transport committee, said there weren't enough police on highway to enforce traffic laws and that 8,000 traffic officer posts are vacant.
Paul Swart of the opposition Democratic Party called for improved policing, more frequent roadworthy tests and limiting the number of hours bus drivers spend at the wheel. Some crashes have been due to drivers falling asleep on long-haudrives.
"It is clear urgent action is needed," he said.