Independent MPs very very rarely get elected.
And if they do, it's very much a local/single issue. Also I am wary of the word "independent" in politics. Like all other words in politics, it's not the dictionary definition.
Off the top of my head (and almost to prove a point) I can only remember 2 independent MPs being elected in my life. Marin Bell - who stood against the deeply unpleasant Hamiltons (cash for questions, Tory sleaze mid 90s vintage) and the guy (a doctor if memory serves) who won Wyre Forest over some issue with a local hospital.
Not quite sure about George Galloway. But that isn't a political comment.
Ken Livingstone was supposedly "independent" when he became mayor of London.