Tania Alexander was born Tatiana von Benckendorff, the daughter of Count Ioann von Benckendorff, a high-ranking Tsarist diplomat, and his wife Maria Zakrevskaya, later known as Baroness Moura Budberg. At age three, Tania and her brother Paul were taken to their father's ancestral Estonian estate to escape the Russian Revolution. The following year, her father was shot dead. The children were cared for by an aunt, and Tania learned English, German, Russian and Estonian. At age 11, she was sent to high school at Wesenberg. Tania spent the summer of 1925 in Italy with her mother and her mother's lover Maxim Gorky, and formed a strong attachment to the writer. Moura Budberg moved to London in 1933 and renewed a relationship with H.G. Wells, and in 1935 Tania joined them. She got a job as an editorial assistant and until World War II, continued to return to Estonia for summer holidays. In 1940, she married Bernard Alexander, a British lawyer. They had three children and lived in New York, Geneva, at Great Haseley, Oxfordshire, and in Knightsbridge, London. In the 1970s, Tania Alexander, like her mother before her, began to translate Russian novels and provide advice to film and theater directors on the customs and manners in them. She worked with Jonathan Miller on his version of Eugene Onegin for Kent Opera and his stage production of Three Sisters; with Charles Sturridge on his adaptation of The Seagull, starring Vanessa Redgrave; and with Jonathan Kent on his production of Chekhov's Ivanov, with Ralph Fiennes and Harriet Walter. In 1992, she produced a new translation of Uncle Vanya for a 1995 film adaptation by Julian Mitchell, starring Anthony Hopkins.
She wrote her memoirs, published in the UK as A Little of All These: An Estonian Childhood (1987) and in the USA as Tania: Memories of a Lost World. In 1990, with Vera Stone, she published the Little Russian Cookbook.