Here we go...

First step was to remove the internal gubbins which I want to keep and maybe make work and put in a clear case so you can see the 55 year old circuit boards, this was fairly easy - the bottom of the casing slides off and all of this can be removed by undoing a couple of screws

The guts

This hole on the original radio is for plugging in an external aerial - for example, if you're using it in a car

Aerial socket...
I found a new (well, old) top panel on eBay, which I apparently didn't take a picture of before starting to mess with. I drilled out the bottom of the aerial socket on it and fitted a 3.5mm audio jack socket that will be the input:
...now AUX in

I decided I wanted to use some of the buttons as play/pause/skip controls, my thinking being a physical button is much better to use while driving along than illegally using a phone and taking your eyes off the road, plus it means everything still looks pretty "vintage" and it's just nice to have the buttons do something. I found out how they work with a bit of research - including this project by George Smart, which I'm basically planning to copy - and the plan is to make my own set of controls so that these buttons do previous - play/pause - next

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Behind that top plastic panel I've made a wooden one (out of a broken storage crate) to attach everything to:

And I've printed symbols for the switches on to blue card to subtly label them and mimic the blue of the original tuning section:
New tuning area background with control labels...
I also added a little strip of plastic (1mm wide x 0.5mm thick Evergreen strip, from a pack originally bought for scale modelling purposes) - coloured red with a Sharpie - to act as a tuning needle. As the radio isn't going to work as a radio this will be left permantently "tuned" to 247 MW - BBC Radio 1's original frequency (more on that later), and - for now at least - the tuning knob will be left as a non-functioning dummy. I was going to glue the red plastic straight to the blue paper, but then I realised I did have room to raise it slightly with a card spacer at each end, so there's a gap underneath like the actual radio. It's a tiny difference but it makes it look more like a real radio when you see it in person.
...and with needle.
Original for comparison

These are the speakers taken out of the old computer speakers from the first family PC (back when computers were big and off-white)

They're surprisingly loud
This is the circuit board from those old speakers (with amplifier, power input, etc) bolted to the top panel so the volume control pokes out in the right place, and I'm going to move the power button (that big blue switch) to align with TONE on the top panel:
Big blue switch

MW will, if everything else goes to plan, be a button to switch between two inputs:

(I bought the iPod for testing purposes, figuring that if I manage to make this so wrong that I break whatever I plug into it I'd rather break a fifteen quid iPod touch than my phone or my old iPod classic)
Power/Input

As well as the new top panel, I later found on eBay original tuning and volume knobs and the push buttons for the switches which solved the problem I'd had of finding suitable alternatives. They came rather entertainingly packaged in old cigarette packaging inside a chocolate box (I took a video of unwrapping them, I must add that at some point)

the volume knob was almost a perfect fit to the stem of the control from the old PC speakers - a little bit of tape made for a snug fit, and the tuning knob slotted nicely onto a bit of dowel I found (I would like to find a function for the tuning knob, but for now it's just there for looks)

Next step: actual electronics