Colette - both my two are like this, and it is incredibly wearing, isn't it?
The bad news:
School doesn't help - if anything it gets worse. Because they have to be quiet in school all day, they seem to talk even more the rest of the time!
The good news:
It does give them confidence to talk in school, to ask questions if they don't understand, and this is a big advantage in state schools with large class sizes. A teacher can't ignore/overlook a chatterbox!
It does increase/improve their vocab, and this helps with readings. Ds1 is a fantastic reader, and as Tigermoth said, he can't talk at the same time ... peace at last.
Things that help:
I do try and teach them rules of politeness and conversation, and insist that they take turns with each other, and with me. Sometimes we use a prop (a teddy or something), and you're only allowed to speak if you have the teddy.
Try and encourage her to wait for a short time, and not interrupt - I hold a finger up and say "wait a minute, I'm talking", but ensure I don't make ds2 wait too long, and always praise him afterwards if he has waited patiently.
Don't let her 'drone on' continuously; encourage her to have real, two-way conversations with you, when you give her quality time, and listen to what she has to say. But at other times tell her she should 'witter on' inside her head, not out loud, because nobody is listening.