You have an arc-over somewhere in your power supply system. Electric arcs produce a broad band signal with precisely that noise pattern.
Cracked or dirty insulators on the power poles, transformer with an internal primary circuit fault, loose connections between the transformer and meter, or compromised underground feeder cables that are leaking current between the conductors will probably be the source of this EMI.
Heaven forbid that the source is anywhere in the house, that's a dangerous situation.
Determining where it comes from
Given the noise that can be heard in the video, this should be transmitting a pretty nasty interference on AM radio frequencies to the point you should have no problem using an AM radio as a source detector.
First steps are to make sure this isn't something in the house that is suffering from a loose connection, ground leakage or arc fault. Turn your radio on and with it somewhere mid band between stations, see if you can hear the noise. Now go through the breaker panel or fuse panel and cut power to each circuit till you have cut all power to the house.
If the noise goes completely away from powering off a circuit, then start looking for appliances, switches, lighting fixtures powered by that circuit that that have failures. At this point, if wiring starts being the possible culprit, you're getting into electrician territory, so get a qualified electrician if you're exceeding your technical expertise or what you're allowed to do under your local laws.
Using this method, I had found that the people who wired my house up had used a crimp ground ring to complete a power circuit in the bathroom which explained the radio noise and the dim lighting that would flicker every so often. Removing the electrician's tape off the odd looking connection revealed that the crimp ring (improper use, only supposed to be used in the ground circuit) had worked loose and the copper wire was being slowly eroded from the arcing in the loose connection.
If the power down only slowly diminishes the noise till the last circuit is cut off, then you need to make sure the power entrance and cabling to the breaker panel/fuse panel are intact to clear your residence (qualified electrician time, you do not want to be messing with this).
Once you have cleared your residential wiring, then you need to get the power company involved in hunting down where the noise is emanating from. It's in their best interest to fix it if its a bad splice, cracked insulator or transformer getting ready to blow.
It is unlikely that the chassis is getting "energized" for multiple reasons. First of all, if it was grounded the breaker would trip. Secondly, the power draw of a washing machine would be very dangerous if you touched it. Also, the design of such devices is done to make such accidents rare, otherwise the manufacturers would be facing hundreds of lawsuits. That you see the same thing in multiple appliances makes it improbable that it is current leak. (What is the probability that ALL your appliances have a dangerous current leak? Negligible.)
If you are convinced there is a current leak, it is easy to test. Just touch one end of a voltmeter to the "energized" chassis and the other to a ground. If it reads 240 volts, its energized. According to another post the OP apparently did this test and it turned out negative, confirming there is no hot chassis here, it is static electricity.
The shock is probably due to static electricity. Both washing machines and air compressors will build up very strong static electricity charges due to rotary motion. If this is not discharged by a ground, static electricity will accumulate and charge up any metal on the device. You also see this same effect on cheap, ungrounded shop vac-type vacuum cleaners.
Best Answer
The output appears to be ungrounded or center grounded. It could be a transformer intended for outdoor tools in UK. If there is also a safety ground 3 wire plug, it could be coupling some of the harmonic current from the switch mode active power supply (which should be flowing equally on hot and neutral) on the safety ground. That would be unbalanced current and trip the GFCI. The smaller transformer could be wired with normal grounding or it may have a plastic case. Adding filtering to the mains input could fix the GFCI issue.