I think I see what he means. Apologies if I've completely misunderstood.
He's on the 'vertical stroke' of the 'T' and wanting to turn right, and the junction has no lights.
His question is can he enter the box and wait for a gap in the traffic passing left-to-right in front of him before finishing his right turn maneuvre? i.e. the thing we all do all the time which is to go half-way when there's a gap in the traffic coming from your right and wait for a gap on the left, because you'll grow old and die waiting for a gap in both directions.
Highway Code Rule 174:
Box junctions. These have criss-cross yellow lines painted on the road (see ‘Road markings‘). You MUST NOT enter the box until your exit road or lane is clear. However, you may enter the box and wait when you want to turn right, and are only stopped from doing so by oncoming traffic, or by other vehicles waiting to turn right.
So the $64,000 question is what is meant by "oncoming traffic"?
Does it mean only traffic travelling in the opposite direction to you, as implied by the drawing in the HC, or could it include traffic coming at you from your left?
Has this ever been tested in court/tribunal?