If working on valve/tube gear you should ideally have a fully insulated bench surface (wood is OK if dry) and an insulating floor or mat where you stand or sit. Definitely don't stand on concrete.
The thing you absolutely don't want to have, when doing any powered tests, is any part of your body earthed. No matter how careful you are there is always the risk of touching something with 500v on it, and yourself being earthed is the difference between, 'Ouch' .. and being put in a 6ft hole in the place the current through your body returned to.
It follows that earthed test equipment is a personnel hazard when working on exposed high voltage. Don't touch metal knobs or panels, or earthed scope probes if you can avoid it. I really wish scope manufacturers would change their ways over this. Having an earthed probe in your hand is about the most dangerous thing you can do when testing live high voltages. Particularly if it's in the other hand, not the one which gets the shock.
There have been several deaths on stage through a performer holding an earthed metal microphone in one hand and playing a guitar in the other connected to an amplifier whose earth had come off and touched the live. It's the hand-to-hand shock which is most likely to kill since it goes through the heart muscle. Wireless mics have been a huge safety benefit here. Eliminating the one earth prevents the circuit being closed if the guitar becomes live. As have sensitive fuses in guitar leads. (but they need to blow with ~20mA or so to be any help)
Also, an RCD DOES NOT protect you against this risk when working on amplifier guts. It cannot sense current 'lost to earth' if that current came from a transformer secondary. (Though it would help in the stage performer situation)
Fire: In my 40+ years in electronics I've never seen a soldering iron start a fire. They generally don't get quite hot enough to ignite things. Hot air guns are a somewhat worrying issue though; there have been quite a few reported cases of them going out of control and becoming red or even white hot. I'd advise making sure any such tools are unplugged when not in use. (On some models the on/off switch is not a proper mains switch and should not be relied on)
Safety is achieved by understanding the risks.