While DAB may be grotty, do you have any digital TV equipment (Freeview box, FreeSat, Sky or Virgin Media) ? At least with the first three (not sure about Virgin) you should have options to hear the digital radio stations from the BBC - regional services, unlike DAB, so no local radio included, but still it is a way to hear 6 Music and Radio 4 Extra (even if Ambridge Extra is not something you will listen out for).
Frimblypoo - even with poor broadband service you should be OK for iPlayer (at least for the radio services). ... my landline was installed (OK - enabled) in February 2010 and I had ADSL from March. However the speed dropped from 2000 kbps to 200 kbps (and when it rained, I could lose internet and voice calls for up to 5 days at a time).
The iPlayer test page showed 3 red lights (for HD video, video and something else) and 1 green light for radio service at 128 kbps. My connection was able to give me 160 kbps download speed, and while frustrating not to be able to see any video clips (off YouTube even) without it being start- stop- start- stop I could download some items to view - such as Click, the gadget show they do on BBC News at weekends.
After many faults, some reported, an engineer came one Saturday and had gone up his ladder before I opened the door, as he spotted the dropwire from the gutter to the ground had perished insulation. Fitted a new master socket in my computer room upstairs and I get download speeds of up to 2500 kbps.
I would urge you to consider further checks (post in geeky_stuff maybe!) and it could be that your broadband connection can be speeded up...