So the night tube finally started tonight on the Central and Victoria lines. The fares are just normal off-peak fares, including connecting onto any of the through the night National Rail services. Capping also applies, mostly linked to the previous daytime. The detail is as follows:
If the time of touch in at the start of the journey is before 0430 then the whole journey will be treated as part of the previous day and will count towards any cap accumulated for that day.
If the time of touch in at the start of the journey is from 0430 or later then the journey is treated as part of the new day. As the new day is a weekend day the off-peak cap (if applicable) counts straight away. Fares are still off-peak of course.