Is there any way to stop the radio turning off as soon as you press the engine stop button ? My previous BMW X3 would stay on for ages to allow you to finish listening and only shut down the display as you locked the car from the key fob .

This applied to the earlier cars. Don't know if still so for the later ones:

"Listening to Radio with the ignition
switched off
With the ignition switched off, (ignition key
turned to position 0 or removed), the radio
functions remain available for approximately 20
minutes.
When the ignition is switched off, the unit is also
switched off.
To switch the unit on again, press the 'On/off,
volume rotary control' (17) or the 'Audio' button
(5).
NOTE: The unit cannot be operated via the
multifunctional steering wheel when the ignition
is switched off.
To protect the battery, you should always switch
off the radio when leaving the car." John
2008 Stornoway Grey 3.6 Tdv8 Vogue
2005 TD6 Java Black Vogue - Written off!!
GAP iiD BT
2003 Discovery TD5 Auto, Nanocom Evolution - gone to a new home!
MasseyFerguson 152 - No electronics!! - Sold

On the MY17, the Audio doesn't turn off until you open the door to exit the vehicle. No idea on how this works for earlier models. Paul

MY17 TDV6 Autobiography In Carpathian Grey With Cirrus Interior

"unfortunately" mine is a 2015 so it has the original design radio . Just thinking aloud I wonder if one of the devices used to keep a dash car running would power the radio for a few mins ? Probably wouldn't have enough power ??