Some things have been around for longer than you think, box junctions since before the not young Mr Mustard passed his motorcycle test in the 1970's.
The above historic footage shows us perfectly how to approach a box junction and of course, back in 1957, there wasn't all that much traffic on the road.
Fast forward to today and the delightfully named Bob Christmas, a driving instructor, gives us some perfect demonstrations of how to drive and deal with yellow box junctions (he was in Boston, Lincolnshire at the time, traffic does get quite heavy in the part of town).
Just don't let yourself drift into the box whilst not really paying attention. Look ahead, think & act accordingly, you are meant to be driving which involves taking decisions.
Think of the leading edge of the box as a stop line. Just stop and wait for the box to clear. Do not worry about the people behind you as they won't pay the £130 penalty charge that you receive in the post. You will have to pay it.
More often than not Mr Mustard will have to tell you to pay up and not fight. Best avoid that problem by stopping and making sure your exit is clear before proceeding.