Some 240 feature films from 72 countries will screen over 12 days.
Festival director Clare Stewart declared the 2015 programme as "the year of the strong woman".
"I`m thrilled that the opening night film has enabled us to draw attention for what it means for women to be working behind the camera, as well as stoke debate around strong roles for women and girls in front of the camera," Stewart told the BBC.
She described Suffragette as "a film made by British women about British women who change the course of history".
Joining the stars on the red carpet in Leicester Square will be Helen Pankhurst, the great grand-daughter of women`s rights activist Emmeline Pankhurst (played by Streep) and Laura Pankhurst, the great great grand-daughter of the suffragette leader.
`Extraordinary year`
Stewart said the festival`s theme coincided with "an extraordinary year" in terms of the depth and range of roles for women.
Among the strong female roles at the festival are two played by Cate Blanchett.
In Truth, which also stars Robert Redford, she plays CBS journalist and 60 Minutes producer Mary Mapes, who risked her career to find the "truth" and expose a story on US President George W Bush.
Set in 1950s Manhattan, Carol sees Blanchett play a woman trapped in a loveless marriage who falls for a younger woman, played by Rooney Mara.
With female roles in the film industry under such scrutiny, the LFF has partnered with Oscar-winning actress Geena Davis to hold a global symposium on gender in media.
"It will look at what the industry can do to take proactive steps," said Stewart. "One of the things that frequently gets commented on is the difference for women actors in terms of pay grades again men and the opportunities for women directors."
The LFF programme features 46 female directors in the features category. "That sounds great, but`s that only 20% of the overall programme," said Stewart.
"What`s interesting is that once you start looking at the first feature, documentary and short films you see a high representation of women directors which suggests there are barriers for women who are trying to scale up their projects.
"When you are working in the nimble independent sector it is much more equitable."
The festival will close on 18 October with Danny Boyle`s Steve Jobs biopic, starring Michael Fassbender and Kate Winslet.
Other films include the UK premiere of crime drama Black Mass, starring Johnny Depp and Benedict Cumberbatch.
The Lady in the Van, starring Dame Maggie Smith as an elderly woman who lives on writer Alan Bennett`s driveway, will have its European premiere.
Trumbo, with Bryan Cranston and Dame Helen Mirren, tells the story of Dalton Trumbo, the Hollywood screenwriter who was blacklisted after refusing to testify before the House Committee on Un-American Activities in 1947.
Also on the bill are Ben Wheatley`s High-Rise, starring Tom Hiddleston, The Program, Stephen Frears` film about disgraced cyclist Lance Armstrong and sci-fi romantic thriller The Lobster, starring Colin Farrell and Rachel Weisz.
Netflix`s Beasts of No Nation, starring Idris Elba as an African warlord, is among the films in official competition, as is Tangerine - a film about two transgender sex workers on the streets of Los Angeles which was shot on iPhones.
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