She's scored a trio of roles on quality television series, playing sharp Pauline Jameson in Feud: Bette and Joan, devious Marjorie in Sneaky Pete and, most notably, Martha in The Americans, now in its fifth and penultimate season. Her character in the series is ruthlessly exploited by Clark Westerfeld - Clark being one of the more stolid aliases of Soviet agent Philip Jennings, played by Matthew Rhys.
Fans came to adore Martha. "Alison is constantly surprising you with her wisdom, her sense of humour, her overwhelming dignity," observe executive producers and showrunners Joe Weisberg and Joel Fields. "Her dedication helped transform the character into the complicated woman audiences came to love."
That success would take so long to come to Wright was predicted by early colleagues.
"As a young actress, everyone thought I would come into my own when I was much older," she says. "I think probably it was because they thought I wasn't beautiful."
"I never thought I'd be in film and television," says Wright, who always longed to be on the American stage. "I didn't think that people who looked like me could be on TV."
She had to wait for the medium to mature before she could land work.
In person, Wright is smarter and lovelier than Martha who, in the pilot script, is described as "very plain". Wright is the un-Martha.
"The hair and make-up makes me look pretty atrocious," she says of the Reagan-era clothes. "Better to surprise people in person rather than to be a disappointment."
I wanted to get to the Lee Strasberg Theatre Institute and learn the Method.
Martha was always destined to last longer than most of the prey of murderous agents Philip and Elizabeth.
Says Wright: "It's nice how deeply Martha has touched so many people, and they can be sympathetic to her plight. Unlike the two leads, she is a good person. She doesn't deserve all that."
Wright is the only child of an accountant father and a mother who did social work with the elderly. Her dramatic tendencies were first noted at a young age, when an aunt said to Wright's mother: "She's either going to be on the stage or on the streets."
She performed in musical pantomimes, took classes in musical theatre, her mother working two jobs to pay for it all. Wright read Stanislavsky and saw the direction her acting would take.
"I wanted to get to the Lee Strasberg Theatre Institute and learn the Method, which was not available in England," she says. "For many people, British acting is taught from all the outside things that a person does. In the Method, you use your own pain and trauma. I've got plenty of that," she says, declining to elaborate.
She moved to New York to study, and waited tables at no-frills burger joints, never at swank destinations. "I worked in Hell's Kitchen and met everyone from Broadway."
She kept acting. Her income was a pittance, she was the poorest of all her friends, and health insurance was long a luxury.
All that has changed. "I have health insurance - for now," she says. She lives in Harlem..
"One day, I'll be rich enough and cool enough to live in Brooklyn," she muses.
• The fifth season of The Americans screens on Sky's SoHo channel, Tuesdays at 9.30pm.