This occured in the UK, so not really relevant to the FAA.

In the US though, yes, the FAA would not have a problem with this. This plane would be registered as experimental, meaning you can install unapproved parts. It does have to be inspected, but that can be done by the builder (not the designer, just the guy who built that particular example), or an airplane mechanic.

I know quite a few experimentals with 3d printed parts (including my own). I don't know any where they are installed in a place where failure would result in a crash. Typically I see them used as convenience stuff, in my case I am using a 3d printed catch to hold my upward opening door while I load the plane. If it breaks in flight, I wouldn't even know. If it breaks on the ground, the door will close.

I'm not sure Gloucestershire is under FAA jurisdiction.

Yes. I mean not this one, but the FAA has definitely approved 3D printed parts. SpaceX's raptor rocket engines, for instance.

Some of the most advanced aircraft engines for commercial airliners contain 3D printed parts: https://www.cfmaeroengines.com/leap

The FAA denying approval to parts based on how it was manufactured and not how it performed under testing would be totally ridiculous.

Lots of F1 parts are 3D printed, as well as many satellite rocket parts still flying. You just need the proper materials.

You may want to ask about the LAA: Light Aircraft Association.

Crash occurred in UK