This sounds like a great trip. My advice to you is to not try to squeeze in everything London has to offer in just 3 days. There is way too much to see and do. Buckingham palace is usually crowded and underwhelming, so is Parliament/Big Ben Westminster Abby (though I did see a peregrine falcon on top of the Abby). Pick a few things and really spend time with them rather than rush around to do it all. One item I really enjoyed was a Thames ride out to Greenwich and back, got to see a lot of the city from the water (Also saw a gray wag tail along the way). If you are into theater, seeing Shakespeare at the Globe was super awesome. Same advice for Edinburgh, it is a smaller city, but still lots to do. The castle is a bit over priced (saw a brown tree creeper in the gardens below!) but Arthur's seat is awesome. I agree a trip to Skye is too much, but you could pretty easily get to Loch Lohman or up to Caringorms for a day to see some of the Scottish Highlands.
Counter-point: If seeing a bunch of different places is more important to you than going through all of the minutiae of London, then don't spend more than three days in London.
The first thing you need to figure out when planning an itinerary is whether you prioritize seeing a few places very well or a lot of places in a much more cursory fashion. I remember a post way back when from Vad where he said visitors to Vienna needed to spend an entire afternoon just hanging out in a coffee shop. Okay, that's great if you live in Vienna, or are a train ride away from Vienna, or are 25 and plan to go to Europe twice a year for the rest of your life. I'll be lucky to go twice in my entire lifetime, and I'm sure as hell not flushing an entire afternoon down the toilet just sitting in a coffee shop. On the opposite side of the spectrum, my in-laws just went to Europe for the first time in their lives, and I don't think they spent two nights at the same place, because they wanted to hit as many sites as possible.
One other thing to remember when planning an itinerary: It's easy to look at the train schedule and say, "Oh, City X is 2 hours away from City Y. I'll get on a train at 8, get there at 10, and have the entire day for site-seeing." While train travel is great in much of Europe, you still have to pack your bags, check out of the hotel, arrange for transport to the train station, get to the train station early (if you're like me and stress about things like that), deal with potential delays, get to your destination city, find transportation to your hotel, check in, and possibly change/freshen up before heading out. That 2-hour trip can easily turn into 5 hours all told and knock out the better part of a day.
As for your specific destinations, I don't have a ton of feedback. London was not one of my favorites, but other folks love it. Paris is a top-three city in Europe for me, if not #1, so I'd be spending more time there. (One note on Paris and London: I did them back to back, and it seemed like the subway stops were much closer together in Paris than in London. Like, if you stopped at the nearest subway station for a tourist site in Paris, you'd be walking a few hundred yards, whereas in London, it often felt like a mile or more.) I did the Chunnel back and forth, and it was very convenient, although you did have to be there an hour early to check in rather than just showing up like you would for a train. Brussels I did only a whirlwind tour, and Belfast I've never been to.
