DH is a Scout Leader and I am the "silent scout leader" so have a lot of experience of organising camps (approx 12yrs)
Initially both DH and I agree this seems expensive. Last years camp for us was £190 per child, and unfortunatly this year we will have to put the price up to £210 as we no longer have access to a van for kit transportation. We take approx 20 scouts away and yes more children equals cheaper cost. For example the cost of an activity is often per hour and therefore cheaper for a Troop of 20 than one of just 10. Things to take into account when costing a camp
Site fees - As you've obviously researched £2.50-£4 per person per night. And thats for all campers so include Leaders
Activity costs - Some activities are recomended to last 2 hours not just one, or the Scout Leader will prefer to do a longer session
Food - we try for £4.50 per person per day. We've learnt not all "Value" brands work well when cooked over open flame so some food is more expensive
Transport - Hire of minibus is our main cost. If Leaders are transporting then you won't have that cost but expect 40p per mile for petrol. How is the Kit getting there? Van hire again is expensive
Running costs - Gas for the cooker, expect to pay £20 per bottle. Lanterns run on Petrol, and again fuel needed for cars that have to go out to do daily shopping.
Recce visit - The Scout Association insist that you visit the campsite before camping there. You need to check the suitability of the site/activities, suss out the nearest Supermarket/Petrol Station/Hospital
Hiring of kit - we don't have a big enough marquee for our Troop so hire one in from another one. If your Troop don't need to hire any in, money may be put towards the upkeep of the Kit.
Cost for the Day Out - Sounds like your Troop have a cheap day out. We tend to go to a theme park, again cost of which is included.
Leaders - The total cost of camp will include Leaders. We don't take part in activities but still pay site fees and food for them all. Leaders take a week off work voluntarily and therefore we don't expect them to pay for their food. (however any extras like "nice" snacks and beer for when the kids go to bed come out of our own pocket)
We went to France 3 years ago, the cost of which was going to be large so we took part in fundraising (bag packing/car wash/race night). All Scouts helped out wether they were going or not and the money raised went in the Camp money pot. Any International camp, like I guess Wings is, will be expensive for the overheads such as phone costs and possibly paying staff to man a main "office". It's why DH refuses to take our Troop on one.
As my DH has just said to me, if you are still a little at cost, ask the Leader to justify it. He is more than happy to show any parents who ask, our Excel chart showing the breakdown of cost.
We've personally found that our local Schools offer similar trips to ours for the same cost but for only 3 days compatred to our 7. They have to cover staff salaries.
We do offer weekend camps during the year too, no activities just backwoods style of camping, for just £15.
Hope all this helps