Hmmm - I'm planning a trip for 7 adults for three weeks next June in Scotland, and it's only running $3300 per person, which sounds well within your budgets. That's including airfare, B&Bs, budget food (pubs and such), rental cars, ferries, etc.
Check out my plans if you like:
www.greendragonartist.com/STindex.htm
Here is an article on Europe trip planning - basic, but has some budget tips.
http://www.greendragonartist.com/articlesEurope.htm