The No.4 rifle was built in two marks during the war, No.4 Mk.1 and No.4 Mk1*. Rifles of either mark noticed to be above average in accuracy during test firing would be set aside as candidates for sniper rifles, worked on to further improve the accuracy (bedding, trigger) and fitted with scope mounts and scopes and given the "T" designation.
The other marks of No.4 were post WWII, when the way the trigger assembly was attached to the rifle was modified. This new variation was designated No.4 Mk.2, and when any Mk.1 or Mk.1* was modified during an FTR (rebuilt at arsenal) to have the new trigger mounting the Mk.1s were restamped Mk.1/2 and the Mk.1*s were restamped Mk. 1/3.
I think there were enough sniper rifles left from the war that they never had to make any out of No.4 Mk.2s and if a T ever needed FTR treatment they probably wouldn't have changed the trigger so it wouldn't have become a /2 or /3.