Lisa Marie Smith, 20, was stopped by Thai officials as she got on a plane bound for Tokyo on Monday. It is not known how much of the drug she is alleged to have been carrying.
A Foreign Office spokesman said it was thought Ms Smith was on holiday in Thailand. British officials in Bangkok were hoping to see her as soon as possible.
He added: "Our first concern is her welfare."
Ms Smith is being held in Bangkok but the spokesman said it was not known when she would appear in court.
Her father is believed to be a businessman based in Hong Kong but although she holds a British passport, the Foreign Office contacted other members of her family in Australia.
Last night Ms Smith, dressed in a blue T-shirt and blue skirt, was locked up in a police cell with seven others.
In Thailand, drugs trafficking carries the death penalty, but no Westerner has yet been executed for the offence. After a gap of nine years, executions were resumed two weeks ago.Reuse content