The Foreign and Commonwealth Office confirmed Britons were among a number of victims in the crash, which happened in a town roughly 30m (48km) north of the holy site of Mecca.
A spokesman said: “We are supporting the British families of those who have died and those injured following a serious road traffic accident near the town of Al Khalas, Saudi Arabia.”
The coach was travelling between Mecca and Medina on Saturday afternoon when it was hit by the tanker, which then caught fire and set the coach alight.
One of the victims was a woman in her 60s from Blackburn and three others were from Preston: an elderly man, an elderly woman and her son.
Their families are planning to fly to Saudi Arabia in the next few hours.
Saudi Arabia’s embassy in London said in a statement: “The royal embassy of Saudi Arabia in London is working with (Britain’s) Foreign Office to issue emergency visas immediately to both the relatives of the four pilgrims who died as well as to families of the 12 British pilgrims who were injured.”
Many of those injured suffered fractures and are being treated at a hospital in Mecca.
The driver of the tanker is also said to have died.
Gulfaraz Zaman, director of Blackburn-based Hashim Travel company, said: “The coach driver said they were travelling in the opposite direction to the petrol tanker when a car overtook the tanker and he had to move in to the side of the road a little to let it through but then the petrol tanker hit the coach which caught fire.”
More from Saudi Arabia
Saudi king attacks Trump over Israel embassy move
Black Panther will be the opening film for first Saudi cinema in 35 years
Saudi Arabia signs preliminary deal to buy 48 Typhoon jets from the UK
UK senses opportunity in Saudi Arabia’s reforms
Saudi prince poses with PM on controversial visit
May voices Yemen concerns after Corbyn accuses UK troops of ‘directing’ war
The travel company specialises in arranging Hajj and Umrah pilgrimages, which it says it has done for 15 years.
Muslims are obliged to undertake the annual Hajj pilgrimage, which is later this year, but the Umrah pilgrimage is optional and on a smaller scale.