arthurdentpc, there are plenty of areas with DAB but no BBC Reception.... Digital1 Network has much higher coverage of Great Britain than BBC National DAB does.
Having multiple radios of varying quality (basically the newer the radio the more sensitive it is) I can't give a straight answer - instead I choose what I can listen on all my non-handheld radios at homes - therefore I've voted for "around 30"...
On my HiFi tuner I find 29 stations, they are NOW Nottingham and Digital1 Network, and for most of the time BBC National DAB (I now have a dipole aerial indoors which has improved reliability of BBC National DAB, so I'm hoping it won't be missing for half the summer!)
In the car I get NOW Nottingham and Digital1 Network, with NOW Leicester and BBC National DAB being intermittent, and very occasional availability of MXR Yorkshire.
My handheld set gets 17 stations (Digital1 Network and NOW Nottingham) in usable quality, with some faffing you can get BBC National DAB in a fixed position (i.e. at my desk at work) but someone walking past is enough to knock that out.
The surprise of the bunch is my bathroom radio (Roberts RD-49) which gets solid reception of NOW Leicester most of the time - a feat no other radio manages - alas the vast majority of that multiplex duplicates NOW Nottingham so isn't used anyway.
My parents DAB radio gets around 40 stations in the kitchen, and 50 upstairs (MXR North West, Digital1 Network, EMAP Central Lancashire, BBC National DAB being the core, with EMAP Liverpool upstairs too) - My Pocket DAB gets ~40 stations there.