I believe the Birmingham test is set by the same people/similar to the Warwickshire one which my two girls have taken. It is supposed to be tutor proof, which ought to mean that it is too unpredictable to recommend a particular practice approach, but I suspect that any test can be prepared for up to a point, and in the couple of years since it has been introduced here, the pass mark seems to have steadily risen.
The Warks test is in 3 parts, verbal reasoning, non-verbal reasoning and maths. Its main feature appears to be a breathless pace. DD1 took it in the first year that it changed from a more predictable VR format, and it did seem to throw a lot of carefully-tutored children. We weren't that committed to it, and DD winged it on a couple of Bond books, a devil-may-care attitude and a complete lack of expectations.
DD2 took it last year, and I did more with her as she wanted to join her sister. I used the Bond books as a basis, but tried to find exercises in different formats, including puzzle books. I particularly worked on her speed, as she's a bit more ponderous than her sister (though a lot more thoughtful). She'd had some tutoring for her maths in year 5 as she had a bit of a crisis of confidence in year 4. I didn't flog it too hard though, as I wouldn't have wanted her to get in solely on preparation, even if that were possible. She didn't get in, and I suspect that's actually a good result for her.
Strong maths is important, I think - DD1 went into the test on about level 5C/B and didn't do particularly well in the maths part of the test, though it's one of her strongest subjects now; DD2 went in on about 4A and did quite poorly. Their VR and NVR scores were pretty much as I would have predicted, according to their natural aptitudes, so I think it's probably quite a good test, as they go.
Here is info from the 11+ Forum on the Warks test; it's a bit more detailed than the info on the Birmingham test, but it does appear to be broadly the same.