Quote from an RAC article, April 2018, suggesting that cyclists may only enter a cycle box from the left. I can find no reference to this elsewhere online or in the Highway Code.
"As with most similar issues, there are contributing factors on both sides.
There are occasions when motorists flout the rules and drive straight up to the second solid white line at traffic lights, but there are also occasions where cyclists enter the zones illegally in the first place.
It is only legal for a cyclist to enter an ASL from the break in the solid white line, usually found as a small gap on the kerb-side edge.
So if a cyclist enters from the centre or right, they are committing an offence and potentially putting themselves in danger by weaving in and out of traffic to get there.
The Cycling Embassy acknowledges the negatives of ASLs, stating there are many disadvantages including the fact that they may encourage people to filter past traffic when it may not be always safe, and to position themselves in dangerous positions in front of HGVs and other vehicles with poor visibility."