Sorry...

The CurrentPage object itself is always null, not the properties.

In default.aspx (startpage) I have to write:
PageData startPage = new PageData(PageReference.StartPage);

PageData startPage = CurrentPage <- does not work.

I have also tried copying web.config from a working project (not migrated) and have made sure that the correct assemblies and versions are accessed.

The problem occurs on every page with/without masterpage and even if all I do is:

public partial class defaultRedesign : TemplatePage {
protected void Page_Load(object sender, EventArgs e) {
Response.Write(CurrentPage.LinkURL);

This is EPiServer 5.2.375.7 (due to migration).