Hello,
First of all I'd make a written complaint to the dealer. Preferably a printed one and make them confirm they've received it. Probably also in the UK there's also a law that a company needs to answer such complaints within a period of time, if they don't it means they accept the claim
But of course that's theory.
As for the radio, it looks like it's something inside the radio itself. CD is laser (= heat), but also vibrations. Both could possibly cause the radio to switch off.
Vibrations can be eliminated in my opinion, as usual driving would also cause even stronger vibrations.
I'd disconnect the radio from the wiring and leave it for some time (you could also press the buttons after it has been disconnected to discharge the residual current from the capacitors) to reset it. Probably won't help, but it costs nothing, so you could give it a try.
To take the radio out of the console, you'll need some special tools of this kind:
Car CD Radio Mp3 Removal Release Keys Stereo Extraction Tools Pins. Radio CD Mp3 Removal Keys. These will release your factory fitted Radio. 2 Piece Radio Removal Pins Keys. Simply slide into the required position to allow easy removal of your radio.
www.ebay.co.uk
It can also be done out of a drycleanings' hanger
When disconnecting the loom from the radio I'd check if the plug sits correctly and examine the visible part of the wiring looking for possible short to ground somewhere. It also could be a cause of such behavior, but again - probably will also happen when listening to the radio.
Assuming you don't want to repair the radio on you own or pay for the repair in a specialized shop, you have 3 possible solutions:
1. buy a used radio (with code!) for the same model (starting from around 40 GBP for one with no code on ebay.co.uk), replacement should be plug and play, but possibly proxi alignment in
MES could be needed.
2. buy an aftermarket radio + proper fascia; installation would be required, but it's quite simple if you have manual skills and basic tools; proxi alignment in
MES would definitely be needed.
3. buy a 2DIN android + fascia or a dedicated android radio; 4 GB RAM is the minimum for android to work properly, the FM / AM receivers are usually much worse than on the radios from european makers; the advantage is you could use navigation (google, or similar) and other features, reverse cam, hands free etc; usually they don't come with CDs, but have a flash memory instead, which you could use to store music on; if you buy one with LTE or 5G, you could use spotify (or similar); same installation + proxi remarks as for the 2nd point. I've myself replaced the original radio on my Ducato with a 2DIN android radio and am quite happy with the result.