It got worse when her character started two-timing the unfortunate drop- out Egg (played by Andrew Lincoln). "People would come up to me and say, `poor Egg. You're moving up in the world and he's not. You're a woman, while he's a boy'. But I liked Milly. She got short shrift and the worst costumes."
But just why did This Life strike such a chord? "The series looked different to anything else," Dhiri reckons. "It captured people's imagination. They were excited to see something risky which also reflected their own lives. It was very honest, too; it showed warts and all. The series could have died a death, but it worked because it was about characters rather than story."
Another reason it worked was because of its, er, up-front attitude to sex and drugs and rock'n'roll. "It was always going to get flak because it had the courage of its convictions. By the end of the second series, the BBC were coming under pressure and started counting the number of swear-words in each episode because we were adding our own."
Perhaps Milly's defining characteristic was her strength, and that quality is reflected in Dhiri's latest TV role. In The Last Train, a new big-budget ITV sci-fi series, she plays Jandra, a mother of two on the run from an abusive husband. With a disparate bunch of other people, she has to learn to survive in a post-apocalyptic Britain after the world is hit by a meteorite. Jandra gets to indulge in a lot of heartfelt screaming on behalf of her endangered children. "Forget about me, but at least take the kids," she implores a man attempting to high-tail it from the survivors in a van. "Give them a chance."
It was Jandra's passion that appealed to the actress. "When someone says, `you're going to play a mum', you get this image of a wimpy woman who lets her kids do all the talking," Dhiri says. "But, of course, anyone who is a mum and has a job has to be strong and have energy. You have to take on all these responsibilites, so you're an ideal candidate for dealing with what comes along. There's no joy in playing weak women. We want to watch people in challenging situations. Look at the Greek tragedies. There's a voyeuristic pleasure for viewers - `what's it like there?' "
Dhiri is particularly glad that she is not being cast along racial lines. "Casting directors are getting more imaginative," she says. "Just because you've got brown skin, it doesn't mean you have to play someone who has a strict dad or works in a cornershop. I'm now getting seen for jobs which aren't specifically Asian."
For all that, Dhiri is not entirely convinced about the wave of "Asian chic" that is washing over the arts at present. "Like the Scots and the Irish, we do have our trendy moments," she smiles. But perhaps it is more a case of "second- and third-generation Asians looking at the arts and saying, `I can do that.' It was never something the first generation wanted to do. If you have to build up networks, you've got more pressing needs. But if my dad hadn't done what he did, I wouldn't be doing this now."
Later in the year, Dhiri plays a futuristic gun-toting cop in a feature film, 24 Hours in London, opposite Gary Oldman. "All the women in the cast were worst with the guns," she beams. "We were using them with a vengeance."
In the meantime, Dhiri says, "I like being a mini-celeb." The only thing she seems worried about is that "in five years' time, when This Life is shown on UK Gold, my daughter will come back from school and tell me `loads of kids said you took all your clothes off, but I said you'd never do that'."
`The Last Train' starts on Wed at 10pm on ITVReuse content