Three others:
Andrewsfield near Stansted - I flew in there once several years ago, it seemed quite nice and there's a little museum there about the guys that flew from there in the war;
White Waltham, west of London. The clubhouse is a pleasant place to sit and watch the world go by...
Elstree, north of London, use as a refuelling/bladder stop (if necessary) for the heli-routes; up the Thames/over Heathrow. But only go with someone that knows the 'routes well.
(You can tell I've done most of my flying in the South East!)
Oh. Just thought. Try Duxford & have a wander around their museum. Or, another fair old distance, I know, the International Heli Museum at Weston Super Mare. They've got a helipad (be sure to get a briefing) and are very welcoming to rotary winged visitors - no landing fee, but they (very apologetically!) ask for an entrance fee if you visit the museum and, when I went, I was shown around by one of their restorers. An excellent little day out.