BNA is a strong domestic market. They badly lag behind in international numbers. Why is that? IND's London numbers are quite a bit higher as are the Europe numbers even with ORD 3-4 hours up the road. History has also proven that adding nonstop service stimulates demand. So if anything the passenger numbers would increase. Possibly significantly. Since BNA is isolated we know that people most likely aren't driving to other airports and having that nonstop service will pull them back to BNA. So being isolated gives a truer number that represents the limited demand for international service at BNA. IND isn't isolated and has a lot of area to draw passengers from. It can draw from CVG when people want a nonstop to London instead of making a connection in CDG, or people in Louisville who normally would just connect somewhere else. Or even east side of Chicago suburb for people who don't want to deal with the ORD mess. All BNA can do is hope the route stimulates demand. They won't be stealing passengers from other airports.
I would counter that a couple ways. The first is that BNA's numbers that I have seen quoted are from 2011. In that span of time Nashville has been transformed more than any other city with the exception of Austin, TX. It is quite literally a different city in so many ways.
You mention that BNA is isolated from other major airports, and that is true. However, there are several small (but still significant airports) within an easy drive that do frequent BNA for air service if the nonstop flights are there. Right now, many of those London passengers were going to their own airport and connecting through ATL/DTW/JFK/etc. However, with the addition of a LHR from BNA I really think they will get people driving in.
Huntsville (HSV) - The MSA is relatively small at only ~450,000 people, but it is a very high tech, high travel economy with lots of expense accounts walking around. Lots of R&D, government contractors, and military travel. It is less than a two hour drive from Huntsville/Decatur to BNA, and there is already a culture of driving to BNA for nonstop flights (I did it for my honeymoon actually).
Knoxville (TYS) - MSA is moderate in size with ~850,000 people. BNA will capture a majority of the London traffic. Knoxville is already culturally tied to Nashville, so people will choose it over CLT if they can.
Evansville - MSA is small but travels a decent amount to BNA. My last flight had a couple that we spoke to that drove from Evansville to BNA for a flight. Evansville is closer to BNA than IND by 20-30 minutes.
Elizabethtown/Fort Knox - Small MSA of a little over ~110,000. Essentially 100% of the traffic would go through SDF previously, but travel time to BNA is only an hour and 20 minutes further than SDF. I suspect that a good chunk of that traffic will drive to BNA.
Jackson, TN - Small MSA of ~110,000. I lived near there 12 years ago. BNA will get essentially 100% of the Europe traffic from Jackson despite it being closer to MEM.
Chattanooga - MSA of 530,000. I would guess the vast majority of the Europe traffic goes to ATL or connects. There are already ten daily shuttles driving people to BNA from Chattanooga. A nonstop flight from BNA will attract a majority of those people looking to go to London from Chattanooga.
All told, there is the rough equivalent of another Nashville CSA that will now fall into the catchment area of BNA for London flights that was previously using their local airports or were travelling to SDF, IND, ATL, MEM, or TYS.