Ok, here are two screenshots - not London, but showing the same issue elsewhere, with EFB2 is displaying a much larger block which is actually several much smaller sectors. Often this can result in you thinking you're flying into an area with coverage that you need to contact (which as happened to me last night) is sometimes not covered at all, or other times like shown below what is shown as single block is actually made up of multiple smaller blocks which are all online, which results in the mess of frequencies you can see at the bottom in the ATC Ribbon, many of which you will never come into contact with, but reduces the usefulness of the ribbon to almost zero when it occurs.
If any of these individual sectors logs off, EFB2 will still continue to show the same sized polygon on the map for coverage, despite the gaps which are accurately shown by VATGlasses (and other tools using the same API) - you can actually see this below - at the upper right, EFB2 is showing a sector that isn't actually online (and doesn't appear on VATGlasses)
It seems like EFB2 doesn't differentiate between individual sectors and the entire FIRs
It is not possible to get VATGlasses to hide the traffic, but I believe that the traffic shown in the screenshot included below is more than sparse enough compared to the original poster's sceenshots to clearly see the issue (helped in this case by the different sectors being colour coded, vs single colour in the original screenshots)
For EFB2 thankfully I was able to just disable traffic entirely.
EDIT:
I managed to get a screenshot showing London with less traffic, EFB2 shows the entirety of southern England as covered, VATGlasses shows the (correct) lower coverage. Each coloured section is also on a separate frequency.