I haven't been able to find much info on the Trent Valley Way; mostly on local government sites.
I have only one map that covers the area, OS Landranger sheet 128, and the TVW is not shown, but there is The Way for The Millennium which follows the Trent Valley near Rugeley and Burton-upon-Trent
There are also some other Ways that could be interesting to do, such as the National Forest Way and The Ivanhoe Way
But you don't need to be spoon fed with a named, waymarked route. England has a huge network of footpaths, why not get some maps and work out your own route? It should be a bit easier as you already have a line to follow and rivers usually have paths near them and connecting the local villages
Go to your library, and if you need to buy them, this place is as good as any
www.dash4it.co.ukAh! I've just found the Trent Valley Way on this website
www.ldwa.org.ukThey show details like a map, waymark symbols, start & finish, and contact details, but it only runs from just east of the M1 near Nottingham to The Humber
Be warned; Newark-on-Trent has horrendous traffic problems at the moment as they are re-doing the sewers.