Ok, I found the manual at
http://www.robertsradio.co.uk/assets...g_SOUND_41.pdf
You are right - there is no external antenna socket.
(that saved me misspelling "aerial"

) .
Unfortunately, without taking the radio apart, invalidating the guarantee, you can't efficiently couple an external aerial.
I took my old Sainsbury's DAB radio apart and did this after the guarantee ran out - requires some electronics and soldering skills too.
Here's where I described this :
DAB radio works better with aerial down
You would be better off with a model that has an external aerial socket fitted as standard.