I've just looked up the Blackheath to Liverpool journey (for next Saturday) on NRE. Where TfL gives the 16:15 Blackheath -> Charing Cross, NRE gives the 16:04 Blackheath -> Victoria. Both however give a tube journey arriving Euston at 16:52.
Just realised that of course I wasn't comparing like with like: the TfL journey was produced from a query for arrival at Euston (Underground platform) by 17:00, the NRE journey from a query for, in effect, connecting with the 17:07 Euston departure.