It typically costs us in the west a significant amount more to fly to Europe than those folks who live in the east. I've been doing a lot of price comparisons and found some shocking differences for my 6-week trip May 1 - June 12, like +/- 40% price differences between cities. I think the reasons have to do with competition, or lack thereof.
I just did some looking for your dates and itinerary and the prices were not that different between RT Salt Lake City (SLC) to London Heathrow (LHR) and multi-city. You can take the new SLC-LHR non-stop on May 1 and get a 1-stop back from Edinburgh (EDI) via Paris (CDG) for almost the same price.
Delta starts that non-stop service from SLC to LHR on May 1st. Flying RT would cost you $1474. Flying multi-city would cost you $1480. RT Seattle (SEA) to LHR is $988. Multi-city SEA-LHR and EDI-SEA is $1269. That 1-stop return flight goes though JFK. And, of course you have to get to and from Seattle.
All these options were through Google Flights. I've tried many other online resources and find it the best. Personally, I'd never buy a ticket through any organization other than the airline itself. It is truly not worth the potential surprises and hassles.
Take a little time to play with your options on Google Flights. Please be aware that there will be some cheaper flight options, BUT they all seem to have at least one stop and take much longer than the 9-10 non-stop hours from SEA or SLC to London or the 14 hour 1-stop flight EDI to SLC. When you see a $400-$500 lower price, note that you could have 2 stops and be spending 30 hours to get to your destination. Definitely not worth it.
However, you might see some cheaper options using different dates that would be acceptable. You might consider a hop from Boise (Pocatello and Twin Falls are way too expensive) to Seattle. Delta has one, operated by Skywest (you might have my son as your captain) for $206 RT on your dates.
Oh, one thing I almost forgot. You can save your potential itineraries on Google Flights and check to see if prices are changing. Also, when you click on the date box to put in your dates, you can choose Flexible Dates. That will display a departure and return grid with prices where the dates intersect. If you are flexible, this is a good way to see some different days to fly on for cost savings...or not.