Nigella Lawson has been invited to apply for a visa to travel to the United States just days after she was stopped from flying to Los Angeles.

The 54-year-old was prevented from boarding a flight at Heathrow on Sunday, apparently as a result of comments she made about taking drugs while giving evidence in the trial of two of her staff accused of fraud.

But the US embassy in London said on Thursday she had now been invited to apply for a visa and promised the matter could be "handled routinely and expeditiously".

At the trial of two former personal assistants of her and her ex-husband Charles Saatchi, Lawson admitted taking cocaine.

The mother-of-two told jurors she took the class A drug twice, once with her late husband John Diamond when he found out he had terminal cancer and again in 2010 when, she said, she was being "subjected to intimate terrorism" by Saatchi.

But she told the court: "I have never been a drug addict. I've never been a habitual user."

A spokeswoman for the US Embassy said: "There are several ways of legally travelling into the United States and Ms Lawson has been invited to come to the embassy and apply for a visa for travel to the US. We understand she has professional requirements for US travel and these matters are generally handled routinely and expeditiously, so stand by."

The spokeswoman said the embassy was unable to comment on the reasons that someone might be turned away.

A witness told the Daily Mail Lawson attempted to board a British Airways flight from London on Sunday morning but was turned away. "She didn't seem to say much but she did not look happy," the onlooker said.

The US Department of Homeland Security told the Mail that foreigners who had admitted drug taking could be deemed inadmissible. However, Lawson has visited America since the court appearance.

Lawyer Susan McFadden, who specialises in US immigration law, said Lawson could have been unlucky because her fame had drawn attention to the comments in court about drugs.

She explained: "In order to travel to the States without a visa on the visa waiver programme one has to obtain Esta (electronic system for travel authorisation) authorisation.

"As part of that, one has to answer questions about whether one has been arrested or convicted for an offence involving moral turpitude or in relation to a controlled substance. Someone in Lawson's circumstances could tick no.

"But the problem comes when one also has to answer a question as to whether you are a drug abuser or addict. The question of who is a drug user is a difficult one and is supposed to be directed by regulations set out by the Centres for Disease Control and Prevention in Atlanta.

"Typically, any person who has used drugs within the last year can be considered a drug abuser or addict. It could be because she is unlucky enough to be famous and her admission of drug use made the newspapers. It could be that someone said 'Hey, if she has used illegal drugs in the past year she could be classed as a drug abuser'."

McFadden explained that if this was the case, there were a series of steps which must be taken before Ms Lawson would be allowed back into the US. She would first be advised to visit a doctor who holds a contract with the US embassy in London who would carry out an assessment to see whether or not she could be classed under these terms.

If the doctor says she should be free to travel she could obtain a visa in a number of weeks, McFadden said.

Elisabetta and Francesca Grillo, who worked for Lawson and Saatchi, were accused of fraudulently using company credit cards, spending hundreds of thousands of pounds on designer goods. But the Italian sisters claimed every purchase had been approved by their then-bosses and they were found not guilty.

Police had reviewed the allegations of drug use that emerged during the trial but said no further action would be taken.

Lawson told Good Morning America that having details of her acrimonious split from millionaire art dealer Saatchi discussed in court under the glare of the world's media was "mortifying".