I have been mapping the M608 on a 2-year old Jeppesen chart I have here. If you just consider the centerline of M608 then M608 is fully contained within the Daventry CTA in that area so there's no need for a separate mapping. The map just shows the Daventry CTA with its lower limits and that should be good enough to remain free of M608.
If you want to map it yourself, here's the info from the UK AIP (ENR 3.1)
- From VOR POL to 533328N 0020149W lower limit 3500'
- From 533328N 0020149W to 531050N 0015303W lower limit 4500'
- From 531050N 0015303W to 530345N 0015021W (abeam TNT VOR) lower limit 5500'. This is the leg that seems to cross your route.
However...
The M608 is apparently 10 nm wide (according to the AIP). And if you consider the bit from 533328N 0020149W to 531050N 0015303W (second leg that I wrote down) and extend that laterally 5 miles either side, then the southeastern corner of that leg actually extends laterally outwards from the Daventry CTA at 4500' and actually infringes your route. This will probably be the bit that SkyDemon complains about.
Now to be honest I have no idea about the rules here. It looks like M608 is cutting the corner a bit but as you have noticed, this is apparently not mapped. But since SkyDemon gets its data directly from the AIP, it notices.
I couldn't find any regulations with regards to airspace priority in conjunction with the width of lower airspace routes in the AIP. Perhaps somebody else?
Anyway, the MSA in that area is 3300 feet so I wouldn't worry too much about it and just fly a bit lower. And just west of the TNT VOR (east of Stoke-on-Trent) you would be getting too close for comfort to the Daventry CTA anyway at 5000'.