Very early on, Lesley Sharp made a decision that she would not allow the press to drag her family into her considerable limelight. All this powerful actress – tipped by one director to turn into her generation’s Judi Dench – ever says is that she is married (actually her husband is the actor Nicholas Gleaves, a regular in The Chase and City Lights) and that she has two children. Her reticence means no red carpet invitations for them and no domestic gossip for us. It is sporting, then, that she has been persuaded by our photographer, Kevin Cummins, to pose for The Times in her own, circa 1994, wedding dress.

She says it looks like a meringue. It looks to me like a metaphor. Lured to pose on a tiny stretch of beach beneath the South Bank in London, she resembles Queen Canute, or else a very kind interviewee providing her interviewer with an intro about a woman trying to hold back the tides that can engulf a marriage.

She is not, obviously, illustrating her own. We have been talking about Anne, the fiery divorcée she plays in ITV1’s harrowing new drama The Children. At its centre are two children trapped in a messy, modern matrix of infidelity – the victims, to put it bluntly, of adult selfishness. “All these adults are, unfortunately, acting like children,” says Sharp over coffee at the National Theatre, where she has just completed an acclaimed run in the title role of Simon Stephens’s Harper Regan. “That is the ambivalence in the piece’s title. Who are the real children?”

My only quibble with Lucy Gannon’s drama is that, presumably for ratings reasons, it has been done up as a whodunnit. One of the step-children is killed. But by which adult? Sharp insists that the structure is more complicated than that of a normal crime drama, and that the serial ends ambiguously. Even a clarification from ITV’s press officer that in the final edit the conclusion has been hardened up does not diminish Sharp’s admiration.

“I was,” she says, “very impressed by the script because it wasn’t about a sink estate. It wasn’t about people with no money. It was about people who should be doing better by their children, and who fail.”

Sharp, it should be said, has an enthusiasm for television unusual among our classier thespians, believing it cleverer and more exacting than people assume. Despite rising through the Royal Court in the late Eighties and early Nineties in plays such as Top Girls and Our Country’s Good, she has acted mostly in television over the past decade: Theresa in Playing the Field, Trudy in Clocking Off, the white mother of a black baby in the alarmingly raw Born With Two Mothers, and the psychic Alison in the generally regrettable Afterlife.

When I ask who, when she was growing up in Formby, Lancashire, particularly inspired her to act, her answer cites the most surprising source of inspiration I have ever heard: Dick Emery, a music hall comedian whose BBC sketch show demanded multiple disguises each week. Perhaps it is her unsnobbish interest in popular television that accounts for her special bond with the writer Russell T. Davies, who cast her pivotally in Bob and Rose, The Second Coming and, just recently, Doctor Who. Davies has pointed out one of her key acting virtues: she does not plead with an audience to adore her characters.

In fact, Sharp is unusual in tending to look more glamorous off than on screen, where her perfectly normal nose seems to take on a bulbous, vegetable life of its own. That said, at 44, she has been taking sexier roles. What she loves about Anne, a fashion shop manager, is that she is not “one of those dumped wives who walk around in a tracksuit – the breakdown of her marriage has not defeated her. It has given her this energy.”

It is possible that recent tragedies in Sharp’s life have similarly energised her performances. She recites a toll of family deaths from the past year: her husband’s grandmother; the producer Catherine Wearing, who died suddenly on New Year’s Eve and was a close friend; and her father, aged 91 not long after he lost his second wife. (Lesley’s mother died of cancer when she was 15.)

“It was her death that really tipped him over. Me and my sister had to find a home for him because he was suffering from dementia. We would visit him and he would sit and be fine for a while and then all of a sudden he’d go: ‘Oh God, oh God, oh God, oh God.’ He could not bear the fact that his brain was not working.”

She delivers these “Oh Gods” with the merciless emotional fidelity that can make her performances hard to watch.

She then reveals something that she has not before made public. “I was adopted. And in January my real mother died. So it has really been one of those times when there has been just too much grief. When I started rehearsals for Harper ReganI told Marianne Elliott, the director, that I felt as if I was in a bit of shock and I was terrified I might suddenly start crying and not be able to carry on.”

She explains that her adoption was never a secret in her family, but that it was only after she left home that she met her genetic mother, a working-class woman unable to keep her because the father was a married man.

“It was hard. I think the thing is that any set of relationships has its own complications and ambivalences. Being adopted and finding one’s real mother is never a situation like [Cilla Black’s] Surprise! Surprise! It is never all just great, and it is never just all bad, unless you are really unlucky. If you are actually going to try and understand another person who you are absolutely related to by blood, but have no common childhood history with, you have to be prepared for the connections sometimes to be difficult and awkward. And they were.”

Happily, rather than precipitate collapse, Harper Regan and the support of its small company has helped her in the past months, even acted as therapy. In the play, Harper, the death of whose own father initiates the action, faces her own family’s flaws: a demonised father, a daughter in rebellion and a husband who may have paedophile tendencies. Unlike Anne in The Children, however, she manages to keep her family together. To return to our sumptuous visual metaphor: she takes arms against a sea of trouble. But then, if you had to bet on anyone turning a tide, it would probably be Lesley Sharp.

The Children, Mon, ITV1, 9pm

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