Rubbish radio reception here in my corner of Bognor, but I can't find any clock radios with an external aerial socket. Anyone know of one?

Any radio with a dipole cable antenna sticking out of the back (2 pieces of flimsy wire) can have a co-ax socket grafted on. Try Tesco.

what you mean like a TV aerial socket, BJ?

Try Revo – they also have good customer service.

Exactly. So you can plug your external antenna in. You might need to experiment which wire is earth though.

Pure Tempus DAB Alarm clock radio

Has touch sensitive handle for snooze and illuminating the clock at night.

You can connect an external aerial, extra speaker for stereo, headphones and there's a spdif output, should want to connect to an A/V amp.

Had mine for several years, works a treat and has a great tone for listening to voice only broadcasts.

Are you sure about the aerial socket, Sponge?
The spec just says "The rear of the unit has a total of six connectors, USB (for upgrades) Aux In, 3.5mm headphone, stereo out, Aux out and the DC input"