Overall, I think it’s good, but heavy on cities. (I like your link.)
I assume you know that some of your sightseeing might be a little bit too ambititious, you might end up skipping this or that.
Also you have to allow time for getting from city to city. Are you more of a city-type of person? I see you have Stonehenge put in your time in London, to me this is a good idea, you can get out in the country for a day.
Those kinds of day trips (also Versailles, out of Paris) will give you a bit of a break from the urban scene.

I like it too. I’m a fan of big cities, so this is a trip that would interest me.

A little city-heavy for my taste, but sounds like fun. If you get a nice day while you’re in Edinburgh, I HIGHLY recommend climbing Arthur’s Seat (in Holyrood Park at the south end of the Royal Mile). The view of the city is amazing, and the walk up isn’t hard.

Conversely, if you get a rainy day and are looking for indoor things to do, the Museum of Scotland (on Chambers Street) is fabulous.

I don’t really have much to add, I just wanted to strongly second the suggestion of climbing Arthur’s Seat. Doing that is what put Edinburgh atop my list of places to return to. Also, if you want a little less time in the cities, might I recommend the Western Highland Rail Line (from Glasgow to Mallaig, Scotland)? This trip takes 6 or 7 hours one way, but if you were based out of Fort William the trip to Mallaig would only take around 4 hours. This is as good as scenic train rides get in the British Isles.

ok thanks, this is my first backpacking trip so I wanted to go in the most lively places.

My freind is unsure about how he is gonna meet me from london to dublin. He doesnt really want to fly. Any one know?

How are you getting from Prague to Rome in one day? You are going to have to fly because it is a very long trip. Btw you missed some key places which were way better than London, Amsterdam, Paris and Rome. Check out Budapest in Hungary. I had so much fun there. Also go to Dubrovnik or Split in Croatia. Read up on Ljubljana in Slovenia. Its really nice there. Also San Sebastian, Sevilla and Granada are worth seeing. You can also check out the Pink Palace in Corfu, Greece. Hope this helps!

A couple of points…

London to/from Dublin is easy by train and ferry if you don’t want to fly. However, flying is faster, and usually cheaper.

I’m not sure I’d plan the Notre Dame (Paris) bell tower on a free day. The last time I was there, the line was over 4 hours long on a day you had to pay.