I have been looking at the fares for this line and they are truly bizarre.
For example -
Dalston Jn to Haggerston or Hoxton is £3.50 SDS and £7.00 SDR. To all stations Shoreditch to New Cross Gate inclusive it is £4.00 SDS and £8.00 SDR. But to Brockley Rte Surrey Quays it is only £2.40 SDS and £4.30 SDR. All the way to Crystal Palace Rte Surrey Quays is only £3.10 SDS and £5.30 SDR!
So you can go all the way from Dalston Junction to Crystal Palace for less than the 2 minute ride to Haggerston!
And while the 1 stop from Whitechapel to Shadwell is a whopping £3.50 SDS, £7.00 SDR, the 1 stop from Shadwell to Wapping is only £1.60 SDS or £3.20 SDR. Also the 5 stops from Shadwell to New Cross Gate is also £1.60 / £3.20.
As it is seemingly part of the National Network with no special ticket restrictions advertised on Avantix, I assume that you can just break your journey as normal and thus never ever need to buy the mega expensive £4 / £8 tickets!