Personally, I have found Luton very accommodating in providing zone transits. I have requested Pirton to Hemel a couple of times and had it granted; also other transits have been OK when roughly perpendicular to the 08/26 runway. Cleared altitude has usually been 2000-2400 feet VFR, as this is the altitude I have approached the zone boundary at. Occasionally I have been vectored to avoid landing traffic below me -- presumably in case of a go-around.
I have only had one refusal, when I requested an IFR transit at a busy time.
The roughly direct route from Oxford to Cambridge via the Luton overhead is fairly closely aligned with the runways, so I would not expect such a transit to be approved. However, Hemel to Pirton looks OK. (I speak as a pilot, not an ATCO)