Genghis,
Lasham have no problem with powered aircraft. There are several SEPs based there (& I'm not just referring to the tugs.) Nor do you have to be on gliding business to fly into/from Lasham; Bill Brooks was there earlier this year in a flexwing & he wasn't there for any gliding related purpose.
What they absolutely do not want is to be part of the £100 bacon butty circuit. On a good day (
), Lasham will be launching almost continuously from 10am until sunset (ATC permitting) & any delays are resented. Powered aircraft, particularly visitors who aren't used to operating @ Lasham, inevitably do delay launches & that's why Lasham is not a drop-in destination.
People with a reason to visit, usually (but not always) a gliding reason, will be welcomed. Casual visitors will be told thanks, but we would rather you went somewhere else.