Indian-born actress Somi Guha, who lives in London, has instructed lawyers to take action after Clarkson used the word "slope", a derogatory term for people of Asian descent, Mail Online reported.

The offending word was used after Clarkson and the show's other two hosts, Richard Hammond and James May, built a bridge over the River Kwai in Thailand. The programme, the last in the latest series, has already aired on Foxtel*.

After the bridge was finished, Clarkson said, "that's a proud moment, but there's a slope on it", as a man walked across the structure.

Hammond replied: "You're right it's definitely higher on that side."

Clarkson has responded to the allegation with a tweet saying: "I'm not a racist. I am currently sitting in a bar with a man who lives quite near Wales."

Guha claimed that broadcasting Clarkson's comment amounted to unlawful discrimination by a public body.

Her lawyers Equal Justice said Guha's action could cost the BBC £1 million ($1.8 million) in punitive damages under equality laws unless it apologised and took Top Gear off the air.

In a formal written complaint to the BBC, Guha said casual racism in the media by established BBC stalwarts was constantly brushed aside.

She asked whether children watching Clarkson use pejorative terms for people of different races would think it was okay to bully and make racist comments.

In a letter to BBC Trust chairman, Lord Patten, on Guha's behalf, Equal Justice said Clarkson and the show must be censured.

"Please process this complaint as a matter of urgency and give due consideration to not recommissioning Top Gear for another series until these matters are addressed," he said.

Equal Justice's Lawrence Davies said the BBC had refused to tackle "serial offender" Clarkson.

"The BBC defends his behaviour as British humour but it is offensive, casual racism being used to boost ratings. It is shameful and makes the BBC appear to be institutionally racist," Davies said.

The show previously got into trouble because of comments about Mexicans.

In 2011, Hammond was discussing a Mexican sports car and suggested vehicles reflect the national characteristics of the country they are from.

"Mexican cars are just going to be lazy, feckless, flatulent, leaning against a fence asleep looking at a cactus with a blanket with a hole in the middle on as a coat," Hammond said.

Clarkson claimed Mexico's ambassador to the UK would not complain because he would be snoring in front of his embassy television.

Mexican ambassador Eduardo Medina-Mora Icaza did make a formal complaint to the BBC and called on the presenters to make a public apology for stirring "bigoted feelings against the Mexican people"'.

Mexican student Iris de la Torre took legal action against Top Gear but did not pursue it after receiving an apology from the BBC.

- Fairfax NZ News

*Corrected to remove reference to NZ screening time.