LTN and STN are probably the easiest infrastructure wise, both roughly 45 minutes to the Olympic site. If your pax don't know the exact dates why don't you look at something like what the others suggested, eg EMA, Manston or even Bournemouth/Bristol and get a chopper transfer to one of the smaller fields close by the site, it may well be easier to get last minute slots for the chopper then for the A/C. Plenty of helicopter charter companies around in the London area and lots of smaller airfields that can accomodate helicopters close to the Olympic park. There was word a while back that a new helicopter site was going to be opened close to the Olympic park, maybe worth a post on the helicopter forum here.
Don't put your pax on the train, it is a nightmare here at the best of times and not an experience you would want to put them through.