Yes, there is such a thing as a best work gun. Yes, a boxlock can be of best work.

We in the USA live(d) in a socioeconomic system that promoted mass produced goods of a somewhat narrow range of quality whereas the Brits live(d) in a socioeconomic system that promoted handmade goods varying widely in quality.

All Brit vendors of guns could get out a best work gun. Because the gun trade supported many makers/workers (outworkers) to the trade. Price for services rendered determined quality of work.

Best work guns were and remain fearsomely expensive. The upper levels of Brit culture were fearsomely wealthy. Best work guns were only one of many best work goods available and needed to maintain place in society.

Brit guns are for the most part true to the grade they were built for. That is, they have grade harmony of wood quality, engraving quality, fit and finish, design, and materials. You rarely see, say, high grade wood on a pedestrian grade gun.

A London style sidelock of best work is both a quality statement and a fashion statement. On the other hand, a boxlock of best work is a quality statement only.