Cheltenham Ladies, Roedean, Benenden and West Heath are well known internationally.
I would say, with the advent of the internet and more particularly, Wikipedia, other girls' schools that would not have previously been known, are gaining greater awareness. For example, most people who are very interested in girls' education would have heard of St.Paul's but that awareness has broadened as a consequence of Rachel Weisz attending the school and people simply 'absorbing' the name of the school as they read her 'Wiki' entry or IMDB biog.
Royal connections certainly help boost the popularity of a school. Since Sophie Winkleman (big Suze in Peep Show) married Freddie Windsor, I have heard that applications have increased there. The fact that it has another pupil who went on to become a professor of English at Oxford probably helps too - it's never easy to determine the exact reason for a spike in demand.
I would be extremely surprised if applications for Marlborough did not surge from international interest as a consequence of Kate Middleton attending the school and parents across the world having easy access to knowledge of where she went to school. To their mind, they want their daughter to have the education of a princess too.
The alumni of a school (royal connections,prime ministers, actors, authors, singers, designers, entrepreneurs) make it desired and if they are deemed to be of a certain class then the school's status will increase by assocation. Its history, how it was established, the strength of its clubs, the number of Oxbridge applications and more superficially the price of the fees and even the architecture determine how 'posh' it is deemed to be. In the past, academic achievements may have mattered less, however parents are becoming more demanding and 'posh' without enough Russell Group and Oxbridge mascots is a concern.
To some, the day schools will never have the cache of the boarding schools that must have been attended by a member of the royal family to have real standing however increasingly, intellectual vigour combined with a few famous Oxbridge pupils give London day schools an attractive, gritty edge. Children now have greater say in where they want to spend their teenage years and they, along with their parents, do their own research. G&L, has been made 'cool' by Lily Cole and Kate Beckinsale, for example because they are attractive, intelligent and have a certain insouciance. Like attracts like -(or what people aspire to)