No need to worry about BB height at Halesowen - I ride with the uni triathletes there, all on road bikes. It isn't the tightest of tracks so you don't need to worry.
If I were to get into track racing (I just ride it occasionally at the moment), I would just get a frame, fork, handlebar and bottom bracket, and then take saddle, wheels*, and chainset off the fixed. I've already got a full set of chainrings and sprockets so there isn't much point doubling up. I doubt my Pompino would be allowed even without the front brake.
*Don't know if commissaires would allow 32h Open Pros...cheaper than a set of tubular track wheels.