Electrical – Pretty big electric shock when touching the lamp

Well, if there is something leaking current onto "ground" and that thing is connected to your metal box, and the metal box is not connected to the ground in your breaker panel, no, that's not great. I would take a multimeter, turn off the breaker to the house, and check the resistance between neutral and the box. If it is large, then they are not not bonded together at the panel, but yet something somewhere is connecting them in your house. Try using a 3-prong tester on some outlets in your house and see what results you get.

There needs to be multiple compounding faults for you to get a jolt like that from the tub. The tub should be grounded to earth, but to give you a jolt, it would need to be instead bonded to one of the mains lines. Since your detector is no longer complaining, it must be bonded to the neutral line. While a bad situation, in normal use there are likely no adverse effects from this.

The other thing that needs to happen is a polarity reversal from either the power monitor or one of the plug adapters. For example, if you accidentally got an UK to Argentine adapter, it would appear outwardly to be for Oz, but in fact the neutral and active pins would be reversed. This too is bad, but also usually no adverse effects are apparent.

Now you have active mains power running down the neutral washer wiring, which inappropriately includes the tub. If the tub were properly grounded and active power somehow came in contact with it, the breaker would trip or the fuse would blow. Having been instead bonded to neutral, and now hot due to polarity reversal, two somewhat innocuous errors combine to become a potentially deadly combination!

First identify which device is reversing polarity. Looking at a wall outlet, with the ground pin on the bottom, both UK and Oz outlets have neutral on the right. Anything that switches sides should be destroyed. Not just thrown out, destroyed, as in render unusable.

The washer should be inspected and the connection to neutral identified and removed. It may be simply a wire with worn insulation that needs to be replaced, or something more intentional. It's impossible to say without inspection. The situation has not changed from before. While the tub bonded to neutral cannot ever be called "safe", as long as polarity is observed, nothing really bad should happen. You can still get shocked from this because the neutral and true ground are likely at different potentials, but nothing like the full 220v jolt you got.