A cross-London journey has no travel time restrictions. The same also applies to tickets to London Underground zones, too. They are all treated as "anytime" for this portion.If you have an Ovalised cross-London paper ticket, am I right in saying the 1600-1900 restriction doesn't apply to the LU transfer?
You could use a Off-Peak ticket restricted in the mornings to cross London at 7am if you'd like, but you can't make your journey on National Rail within the restricted times.
The only exception is Travelcards, where Anytime is Anytime, and anything else* is considered Off-Peak so is valid in the fare zones after 0930 on weekdays (even if it's a Super Off-Peak Travelcard with a restriction like "not valid into London until after 10:45am", you can use it in Zones 1-n from 0930).
* I'm sure someone will find an exception!
