Your plan is literally impossible in 7 days if you want to do anything besides see the airports or train stations. I would skip Austria and Switzerland because they are quite a bit out of the way of your arrival and departure cities. It's a really quick flight from London to Amsterdam on EasyJet although it will still take you half a day with the time it takes to get to the airport early, etc. While you could easily spend weeks in each city, 2 days is absolutely the minimum and remember you have travel time in between so that's really 2 cities, maybe 3 tops.