Time management

Would we be crazy to even consider fitting London, Edinburgh and Paris all into a 7 to 10 day trip?

yes!

Fly I to London and home from Paris.

The Rick Steves philosophy encourages travelers to slow down, spend enough time in each destination to soak up the local culture and really live the life of a "temporary local" for at least a couple of days. If you have only 7-10 days, I would do the entire stay in one country (i.e., not mix the UK and France). Could you have a decent trip by spending 3-4 days in London, one travel day, and 3-4 days in Edinburgh? Yes, especially if you are happy seeing the central city sights and not daytripping out to the countryside. Trying to jam Paris into the mix would just make the whole experience rather frantic and superficial, IMO.

If your trip is closer to 10 days than 7, you could do 2 of the cities. I haven't been to Edinburgh yet(going this summer), but would choose London and Paris if I were you. And agree that you fly into one city and out of the other. Traveling between locations is very time-consuming.

Although a flight will be only two or three hours, you have factor in time to and from the airport, how early for check-in and security - at least another an hour and half or more so a two hour flight could be more like five or six. My rule-of-thumb is any train ride longer than five, maybe six hours, I will consider flying. With your time, stick to London and Paris and take time to really enjoy both cities.

Stick with London and Edinburgh and take the train between them, it's only a little over 4 hrs. 7-10 days is not really enough to comfortably add Paris.

You can't fly from London to Paris in 2 hours unless you're talking about actual flight time. Getting from London proper to an airport, then a couple of hours to clear security and wait for boarding, then landing at Paris airport, then getting to Paris proper, probably closer to 5-6 hours. If you really want to throw in Paris (not recommended on such a short trip), then take the Eurostar train, it's much faster than flying.

I will just reiterate what others have said....the train from London to Paris is approximately 2.5 hours. That's city center to city center. Why fly?

There's enough to do in two cities

Fly into one city and home from another. Dont' waste time backtracking. You can book that using the multi-city choice on most airline or booking websites.

Example Fly to Paris. Train to London. Train to Edinburgh. Fly home from Edinburgh.

I agree with Frank that if you have 10 days you could do all 3 by flying into either Paris or Edinburgh, train to London then train to last stop and fly home from there. If you will only have 7 days then stick to 2 of the choices (or even better just stay in and around London). As others have said I doubt flying between Paris and London will save you any time over taking the train between the two. Don't forget that you usually don't arrive until the day after you leave and you will be jet lagged on that first day.

Additional advice: Flying into one city and home from another is efficient. However, these are not two single tickets. Calculate a single itinerary by using the multi-destination search function on many airline and on-line travel sites.
Advice on train travel: www.seat61.com
Advice on European air travel: www.skyscanner.com
Main point: London and Edinburgh will be more than enough to keep you happy and occupied.

Just keep in mind if you do take the train from London to Paris (or vice versa) you do need to get there ahead as there is passport control/immigration to get thru - you can't just show up 10 min ahead. They do recommend 30 min, but for me it would depend on time of day and year. And I'm risk averse, so I'd give it 45-60min.

Thank you everyone!!!

Whether it is 7 or 10 days, save Paris for another trip. You will have more to see in Britain than time allows already. Enjoy!

In addition to the travel time and cost of adding Paris to your itinerary,also consider the disorienting effect of switching language, currency and culture. We always limit our European trips to one country.

Agree with Bob about the mental labor of switching language & currency, which is why I recommended staying in the UK (England and Scotland). There's enough variety between London and Edinburgh to make your trip plenty interesting.

As for the question of why you are time restricted, I would hope everyone on these forums would understand that many working Americans only get a few vacation days a year. Once you use up some of your days to go visit family or take care of other personal activities, a trip across the Atlantic may have to fit into one work week of vacation.