My dab radio will get R4, world service etc... certainly in this country!
At the end of the day it's still a radio signal, ok they happen to be sending a digital signal so for a given power it has the potential to use a smaller bandwith and go further (some of the modes are even as efficient as CW!

) but the range is still limited by the same rules as any other radio wave.
Don't know if world service broadcasts from Gib or not, I could certainly reliably listen to world service in the former yugoslavia but which frequency would vary throughout the day.
You may also have found yourself in a "skip" or "dead" zone where you are too far away from the station to hear it on ground wave (direct) but too close to hear the sky-wave signal (the one bouncing off the ionosphere before returning to earth).
We are currently at a poor period for listening to distant stations but conditions appear to have passed the worst and are slowly improving (google "sunspot cycle" or pm me for more!) however you should still be able to hear some very interesting stations.
Generally 20meter-ish (14Mhz) is ok through the day and as it gets dark you need to be looking around 40 metres (7Mhz) or even 80 metres (3.5Mhz) certainly last week Radio China International was booming through along with a number of Eastern European and North African stations in the 7.100 to 7.200 range.
If there is a specific station you are after it's always worth going to their site (or even writing to them with old fashioned pen and paper

lol) and getting a list of their frequencies, you can then try them all 'till you find one that works where you are. Also the simple expedient of taping a length of wire to the end of the telescopic antenna and throwing it out of the window or running it round the room can make all the difference to reception

"Tuned" antennas work best but just getting wire in the air always helps, and any wire will do.. mains flex, speaker wire, bell wire, fence wire.. doesn't matter as long as it's available and it conducts
