pardon my lack of knowledge of your part of the world, but what bandwidth is 'Radio 4'? is it the same as 'AM' radio? because cars like the 156 are notoriously poor with AM reception.
from memory, the 156 relies on the rear-window demister as its antenna, so reception isn't flash to begin with. and if a metalicised 'tint' has been applied, it can be worse again. then, if antenna relies on a powered booster - but this has not been connected up - it will be terrible. i can't remember if the 156 uses a +12V booster; if so, it would need to be triggered by the headunit via its wiring/plugs.
as a general rule, alpine headunits have good radio sensitivity. though another possible issue is if the model you have is not a 'euro' version (as opposed to US or japanese), and therefore the radio circuitry is not tuned/tweaked for your area.
so, what can you do or check? depends what you're capable of doing.
*remove the headunit from the dash and check the wiring; alpine's 'antenna output trigger wire' is blue (as opposed to blue/white stripe); see if this is connected up
*if not, check with alfa or research to confirm that it should/should not be; that is, confirm that an antenna booster exists, and needs power from the radio to active it
*check if you have tinted windows, and whether you can determine if it is metalicised
if unsure, or require further advice, i'd suggest going to a specialist car audio store for advice. they may be able to fit another antenna or supply/fit another more suitable booster.
whilst the alpine could be faulty, it would be unlikely if everything else works ok. again, i'm presuming you are talking about AM radio.