Is there a shortcut key to jump to the next result in the output window?
Like F4 in Visual Studio 6 and F8 in Visual Studio .NET.

I normally uses this to walk thru all the results of a find in files (in VS), but can't find a shortcut for it in UE.

Many thanks in advance

Short answer: no (not yet).

UE does not have such a shortcut key for search results in the output window. For navigation you can only use the 3 methods described in the last paragraph of the help about the output window.

You can define a hotkey to switch focus between output window and active edit window in the key mapping configuration dialog - command FocusToOutputWindow.

And Finn Ellebaek Nielsen has written a tool which can help you - see Find in Files -- Increase Edit Window Functionality.

Edit:

Since UE v15.00 there is Ctrl+Shift+Up to go within the document window to previous line according to previous line in output window and Ctrl+Shift+Down to go to next line in file according to next line in output window.

The keys can be configured at Advanced - Configuration - Key Mapping by assigning something different to the commands OutPreviousMessage and OutNextMessage.