Emergency teams were given the all-clear to search the Pike River coal mine in Atarau, on New Zealand's South Island, after initial fears that a build-up of methane could cause a second explosion.
Experts said tests on air inside the tunnels had revealed it was safe to proceed with the rescue operation.
It was unclear whether the men had survived the blast. It is understood that each of them would have been carrying 30 minutes of oxygen, enough to get to air stores in the tunnels.
By daybreak in New Zealand, no communication had been received from any of the missing workers, the company said.
Trevor Bolderson, a union delegate from a neighbouring mine, said he believed one of the Britons was from Scotland and two from Yorkshire. He said the Yorkshiremen had worked at the mine for about 12 months, while the Scot, thought to be 25, had been there "for a bit longer".
Bolderson was meeting with families of the trapped miners at the nearby town of Greymouth this morning.
A colleague of the miners, who are believed to be aged between 17 and 62, said his trapped friends were from a close-knit community and everyone was praying for their safe return.
"They are a good bunch of men – they were laughing and joking when they went down and we want to laugh and joke with them again," he told the Guardian.
"Pray, hope, beg the Lord – whatever the semantics – we just want these men back alive to share a beer or two."
Two dazed and slightly injured miners had stumbled to the surface hours after the blast shot up the 110m ventilation shaft in the early hours. Video from the scene showed blackened trees and smoke billowing from the top of the mountain.
Tony Kokshoorn, the mayor of Greymouth, said earlier that rescuers had been delayed by worries that gas remaining inside the mine could ignite.
Electricity cut out shortly before the explosion and experts believe that failure may have caused ventilation problems which led to a buildup of gas.
"They're itching to get in there and start looking for other people," said Barbara Dunn, a police spokeswoman.
The drama recalls the ordeal of the 33 Chilean miners who spent 69 days deep in a collapsed gold and copper mine.
John Dow, the chairman of the mine operator, Pike River Coal, said oxygen stores in the mine would allow the men to survive for "several days".
The coal seam – about 200m below ground – is reached through a 1.4-mile horizontal tunnel. According to the company's website, the vertical ventilation shaft rises 110m from the tunnel to the surface. But Kokshoorn said it was unclear at what depth the explosion happened, but that the blast had been "very large".
Peter Whittall, Pike River Coal's chief executive, said 29 miners were missing. He added that the operation to reach the men would be different to the rescue of the Chilean miners last month: "We're not a deep-shafted mine, so men and rescue teams can get in and out quite effectively, and they'll be able to explore the mine quite quickly." Whittall said one of the two workers who emerged from the mine had been blown off his vehicle a mile into the access tunnel. The other man had been able to make a call on his mobile before reaching the surface.
New Zealand's prime minister, John Key, said the situation at the mine could be very serious: "The government has told the company it will provide any support that is required. It is an Australian company that owns the mine and the Australian government has also contacted us offering their support [and] assistance."
The energy minister, Gerry Brownlee, said the explosion happened at 02.45 GMT on Friday and the last contact with any of the miners was about half an hour later. They had not spoken to any of the missing miners since then. Brownlee said emergency exit tunnels were built into the mine but he did not know if they could be accessed by the miners.
Pike River has been operating at the site, the largest and most modern in New Zealand, since 2008.
It processes up to 1.5m tonnes of raw coal a year. It is the country's largest single source of coal exports.
The mine's ventilation shaft was blocked by falling rocks in early 2009, delaying mining for months.
The mine is not far from the site of one of New Zealand's worst mining disasters, an underground explosion in the state-owned Strongman mine in January 1967, that killed 19 workers.