I don't recall the BS requiring a load test at all, that was an insurance company requirement, and I think it was different for various load capacities, but it's getting a bit far in the past. I could dig it out, but prefer not to, life's too short. We used to inspect all welds, and load test the crane, but not the lifting lugs on the load, they just got NDT on the welds. This on the basis that any one load would only be lifted a few times in its life. If it was something that was lifted often we'd load test that as well.
BS2573 does not require anything like a factor of 4 on yield, for straight tension it was 1.7, even less for bending. However for something like a tripod which is likely to be abused or unevenly loaded I'd go for more, and 4 on yield is as good as anything else, especially as we don't have coded welders or NDT of the finished product. If you do the sums by BS2573 and the latest BS EN you get the same results, ie if it was acceptable to the old standard it is acceptable to the new one, just a different approach to calculation. The old one de-rated the allowable stress, the new one uprates the loads. In both there are further factors for frequency of use, how often you lift the maximum weight, consequences of dropping it (ladles full of molten metal, nuclear fuel flasks etc) which need not trouble us here. If you are proposing to work up the the allowable stresses you need to be pretty sure you've done the sums in enough detail, but I've never had to resort to FE analysis. It is entierly likely that there is a different spec for stuff like tripods, I think 2573 is aimed more at overhead cranes and the like. There certainly was one for runway beams.
MRC is 'Manufacturer's Rated Capacity', which means much the same as Safe Working Load, but I assume it has some legal wormhole.