The Lea Valley lines had 310s for a short time they worked with 321s in 1989-1990, both were replaced by 317s from WCML. The 315s were there all along but their territory did expand as they mixed in with the 317s.
Some of the 305s headed to LTS for a short while. NSE 312s only ever worked GN, GEML and LTS.
Back to the 710s as per the OP, very nice looking trains, big upgrade on the existing stock which is really not fit for use as inner-suburban people movers. Looking forward to seeing interior shots.