Is it currently possible to upgrade iPhone 4 from iOS 5 to iOS 6? I suspect the answer is a no but maybe there's a trick to upgrade an iPhone 4 (running iOS 5) to iOS 6.1.3?

The phone is jailbroken but does not have any iOS 6 blobs/APTicket saved because (doh!) it's never been on iOS6.
iOS 6 is not being signed for iPhone 4 any longer.

You must upgrade to iOS 7, or more specifically, iOS 7.1.