All,
Thanks again for your help! Our trip went smoothly thanks to the advice given here. Everybody at Southampton was most friendly and helpful! Airside Ops confirmed that they mostly take day visitors but also try to accomodate overnights when possible. Special thanks to TCAS FAN - what a pleasant surprise!
The only (slightly) disappointing thing was that in over five hours of flying from EDHL to EGHI and back, we didn't see the ground once (except late during approach). Flying in the sunshine above a low cloud deck could have been anywhere. But, a Cirrus SR22 Turbo makes a wonderful travel machine...