I've done a forum search and can only find similar issues relating to diesel engined FFRRs.

I noticed that when idling at around 720 - 730 revs (fairly steady according to GAP tool) my car shakes slightly. It's a regular gentle shake, not fluctuating faster or slower. I only have one error code thrown and this relates to the antenna voltage (!?), so I don't think this is related to the shake.

Also, occasionally whilst idling there is a sudden noise from under the bonnet, then it suddenly stops and the engine quietly idles (and gently shakes) for a while, then the noise starts up again for a short time. It's pretty loud. Is this an AC fan or something more serious?

Gap tool reports circa 14 volts being consistently produced.

Does anyone have an idea what the problem might be please?

Try spark plugs and coil pack first.if one of those has fouled the car shudders. You may finds the spark plug well has oil in it from the cam gaskets

Thanks alistairh. Will get this looked at.