Probably because they were radially wired from the fuse box and didn't have a safety fuse on the appliance lead. Ring main plugs cut down the incidence of death by electrocution considerably, consumer units with built in trips on every circuit even more so.
That is a very sweeping statement. The pedant in me has to say that our current system is based on using individually fused ring main plugs and sockets they are not 13A unless you fuse them at that current, other value fuses are available. The ring itself is 30A of course. That is the point, you can fuse down to the correct level for the current required by the appliance. In your welding example you should not have been using a domestic 15A socket. it should have been a higher current cable and socket and fused accordingly at the box.
Always remember, electricity is a lot faster than you and always test with the back of one hand only.