While @UncertainWhatNameToPickHere provided the acting credit and her role as Guy Fawkes's lover, the significance of the woman has not been cleared up yet. This answer contains spoilers (won't put it in spoiler tags though, because it is an old movie).
I would say that while revolution is the main topic of V for Vendetta, the real main motif is love. Guy Fawkes had an idea that he was willing to sacrifice everything for. His biggest sacrifice has obviously been his life. On an emotional side, though, he put his revolution above the woman he loved. And in that woman's eyes you can see the devastation of a woman losing her loved one.
This is parallel to what V did. I would call it altruism in disguise, because V wants to create a better world for Evey to live in by going through with his revolution by sacrificing himself for that ideal. His love for Evey, on the other hand, had to be secondary to his plans and eventual death. Therefore, the first scene is the historical parallel to the main movie.
You cannot kiss an idea, or touch it, or hold it. Ideas do not feel pain, they do not bleed, they do not love.
This quote from that opening scene carries the same message: Even if V created a better world, the one person Evey loved is gone.