There have been a number of franchise scripts written by women. Note that this list only applies to televised episodes. It does not include audio dramas, comic strips, short stories and novels that have had dozens of female contributors, or "lost stories" that were commissioned but not produced. It also doesn't take into account the fact that women have worked in script editing and producer positions in which they made uncredited contributions to scripts.
The first woman to be credited with writing a Doctor Who script was Lesley Scott, co-author of the First Doctor storyline "The Ark".
Although a number of female writers including the fantasy novelist Tanith Lee were invited to write for the series in the 1970s and early 1980s, the next woman to be credited as a writer was Barbara Clegg, who wrote "Enlightenment" for the 20th season.
"Attack of the Cybermen" was credited to "Paula Moore" but this is a pseudonym. Several different individuals have claimed to be Paula Moore, with Eric Saward, Ian Levine and a female writer named Paula Woolsey all cited.
Beginning in Season 22, the husband and wife team of Pip and Jane Baker contributed a number of serials: "The Mark of the Rani", "Terror of the Vervoids" (part of "The Trial of a Time Lord"), episode 2 of "The Ultimate Foe" (the finale of "Trial of a Time Lord") and "Time and the Rani".
"Survival", the final story of the original series, was written by Rona Munro.
Helen Raynor served a script editor for Doctor Who after it returned to TV. She also wrote four episodes: "Daleks in Manhattan"/"Evolution of the Daleks" and "The Sontaran Stratagem"/"The Poison Sky". Raynor also served as script editor on Torchwood and wrote the episodes "Ghost Machine" (Torchwood story) and "To the Last Man" (Torchwood story). Any scripts edited by her (from "The Unquiet Dead" to "Midnight", plus Torchwood's "Greeks Bearing Gifts" (Torchwood story) likely include uncredited content written by Raynor.
The 2011 and 2012 Blue Peter minisodes "Death is the Only Answer" and "Good as Gold" were each written by a team of schoolchildren that included at least one female student, although you might not count an 11-year-old girl as a woman, or these minisodes as episodes.
Catherine Tregenna and Sarah Dollard contributed "The Woman Who Lived" and "Face the Raven" respectively for Series 9, becoming the first female writers for the show since Helen Raynor, and the first of the Moffat era.
In Torchwood, aside from Raynor, Jacquetta May wrote "Random Shoes" (Torchwood story); Catherine Tregenna wrote "Captain Jack Harkness" (Torchwood story), "Meat" (Torchwood story) and "Adam" (Torchwood story); Doris Egan wrote "Rendition" (Torchwood story); Jane Espenson wrote "Dead of Night" (Torchwood story), "The Categories of Life" (Torchwood story) and "Immortal Sins" (Torchwood story) and co-wrote "End of the Road" (Torchwood story) and "The Blood Line" (Torchwood story).
No women ever wrote for The Sarah Jane Adventures, and no women wrote for the first season of Class.