"Best gun" was never exactly defined. It is a catchy phrase that sounds really good in advertising. However, the Brit gun trade did not come to a definition. It was/is generally understood that craftsmen worked to a price and most had enough production capacity to accept orders for less than best work/design/materials to fill their books. That is to say, most craft shops were quite happy and willing to supply whatever quality grade product the customer was willing/able to pay for.
Craft made guns are most clearly understood if you look at three characteristics: Brand Value level (BV), Original Quality grade (OQ), and Current Condition level (CC). BV represents a price premium assigned by the current day market and is not an absolute indicator of quality. OQ is THE indicator of quality; note that it is independent of maker's marque. OQ can often be identified from old maker's catalogues or advertising. CC is entirely dependent on the care and use the individual gun had during its life to date.
"London best" is most usefully understood as a certain style (SLE, stocked to the fences, no thru lumps, high % engraving coverage, high quality (but not necessarily highly colored or figured) wood); and assumed best workmanship. "Best work" should be understood as a gun made to a very high standard and priced accordingly. A "best work" gun can come with any maker's name on it. Many very fine craftsmen worked as out-workers (not a factory employee). Gun shops were typically run by master gunmakers. The Master's job included knowing who did high quality work, what was a fair charge for it, and who was available. Few shops had all aspects of the gunmaking process covered with in-workers at all times; gun orders cycled up and down and workers came and went.
So, the trick here is to learn to identify a best work gun based on examination, not on brand name.