Nathan,
The X shouldn't have a problem there, but with the runway slope it may be limited slightly on hot days when the runway is wet if the winds favor the downslope runway. If you are only going to Nice, then it shouldn't be a problem for takeoff. As long as you don't plan on carrying excessive amounts of reserve fuel into Southend and the temp isn't in the 30s, then the X will work fine. Just keep an eye on the Basic Operating Weight of the X that you plan on using/buying. This is basically the weight of the plane before adding passengers. Since there is a maximum zero fuel weight, you want to make sure that the X you are using doesn't have too much extra equipment installed. I have seen some very heavy Citation Xs that don't allow for a full passenger (8 generally. 9 if you want someone sitting on the toilet) and baggage weight (300lbs). To fill a X with passengers like that means not a lot of personal space onboard. Have you thought about at CL-300 since it is a short hop you want to use it for? It would give everyone a bit more elbow room.