I took another look this morning. It seems to be coming from the wood rail that runs along the top side of the tube frame there, ie under the wrap around red panel. There's a fastener on the RHS of the photo that shows where that rail runs - it's not very wide. I could fasten through the panel to the rail so the panel doesn't vibrate as much but, given the tone and loudness of the noise, I think it's actually the wooden rail vibrating on the metal frame.
Anyone heard of this? No pun intended.