The amp is oscillating. Although it's possible that both are connected, the RF is likely to be a different problem than the hum. 
Grounding ("earthing" - I'm in the USA, and it's hard to change terms, as you know from the opposite direction  

  ) is easiest to understand by thinking in terms of all ground/earthing wires being resistors, not zero-resistance. Any current flowing in a resistor/ground wire causes a voltage across the wire/resistor. If you mistakenly connect some signal amplifying stage to the end of a wire carrying heavy currents, then the stage will amplify the voltage created by the current in the ground wire. The practice of grounding/earthing for low noise is to force currents to flow through their own ground wire, not a ground wire shared with some other amplifying stage. 
The general idea is that the bigger the current, the more you need to return that current back to where it started from, and on its own ground wire. 
Case #1: rectifier current return wire; connect the negative-side return to the power transformer ONLY to the negative side of the first filter cap, and have no other ground wire share any part of the wire going back to the transformer. The rectifier return wire carries the biggest current pulses in the amplifier, and sharing any part of its return/ground wire creates a hum that can't be gotten rid of any other way than proper wiring. 
Case #2: output tube cathode current return "ground"; the cathode currents need their own wire to return to the negative side of the first filter cap. These wires carry a full-wave-rectified replica of the audio in current form, and sharing any part of this ground wire/resistor feeds this signal back into the stage that shares the ground wire. Connecting earlier amplifying stages to this ground wire for their own grounding/current return amounts to feedback, and this, by itself, can cause oscillation and hum.
Case #3: PI and speaker return; the OT secondary carries high currents to/from the speakers. For lowest noise, the speaker currents need to flow back to the OT secondary, and not through a shared grounding wire or the chassis. Nearly every amp uses a phone jack that's connected to the chassis for this purpose. Usually you get away with this, but sometimes you don't and you get hum and oscillation. The PI return ground should be connected to the negative terminal of the first filter cap on its own ground wire. Sharing the cathode ground of the output tubes means the PI is being fed a signal of the full-wave-rectified-audio currents times the output stage's ground wire resistance. Likewise, if the speaker return current shares a wire or path across the chassis with the PI ground current, the PI is being fed a "ground" signal from the speaker currents. 
These are just the high points - and noted in order of high currents through ground wires. If you're thinking that this means that every single ground point ought to have its own ground wire, then, yes, you're right. That is "star grounding". No one has the patience or enough wire to do the full job. Nearly the full effect can be had by clustering all the grounds to one closely-connected bunch of stuff and using a separate wire for that cluster. Clustering the grounds to one preamp tube is an example that nearly always works well. The PI tube is another. 
Star grounding can be shown to be hum and feedback free before wiring. Every other ground/earth wiring technique uses some form of intense thought or luck in combining ground currents that semi-cancel or cause issues below the detectable audio level.
"It's not what we don't know that gets us in trouble. It's what we know for sure that just ain't so"
Mark Twain