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DataFactory.Instance.LoadedDefaultPageData should cover your needs. The new page can be accessed using e.Page["PropertyName"]
And if David's approach wouldn't suit your needs, perhaps you can try something inspired by what Deane does here: http://world.episerver.com/Blogs/Deane-Barker/Dates/2010/9/Automatically-Naming-Pages/
DataFactory.Instance.LoadedDefaultPageData was exactly what I needed. Many thanks.
I want to set default values depending on current user and where the page is created. I have tried using events like DataFactory.Instance.CreatingPage and DataFactory.Instance.CreatedPage but I want to set the values before UI is loaded so the real values will be visible to the editor.