Go DAB, fm is pretty crappy in all cars, not only in z4
FM coverage is actually very good across most of the U.K. (Depending on the station) and is set up for working effectively with car antennas - But, and it's a big but...
Most cars are now fitted with short antennas and an amplifier. The standard Z4 antenna is like this. Fit a stubby and you need a much better rf amp on the much smaller signal that you are picking up. Any minor problems with that amp or with connectors and earthing arrangements will magnify any signal issues and reduce the radio quality.
Having said that, like any broadcast service, there isn't 100% coverage. It's targeted at population coverage, and in some locations, busy roads. The big transmitters like Sutton Coldfield have a good coverage of up to 40 miles but are still unable to reach some valleys and the shadow of large buildings. Only the hillier areas around south west Birmingham might suffer but then there seperate transmitters to cover that area.
Make sure you have RDS on as that supports transmitter switching (Traffic Anouncements are a service on RDS).
DAB is a much more complex signal and needs a good antenna and rf amp to work well. There are however many more DAB transmitters now to cover the weak signal areas. Good DAB radios also support switching to other transmitters as you move from one area to another or even switching to an equivalent FM station if a DAB one isn't available. You usually hear this because the signal timings and decode time on DAB is much longer than FM (and often different on different DAB radios - if anyone wants a masterclass on COFDM coding and decoding just ask).
Reception of most BBC FM around Balsall Common should be good. Some commercial radio stations may not be (they typically use lower transmit power than BBC).
So, if you have problems, check your cabling and amp first. If you have line of sight to Sutton Coldfield you will have a good signal. I can pick up some stations broadcast from there in Daventry in my Z4.