This is worded for the older reader who might not be clued up with current audio technology (which included me before I looked into it).
The technology is by Bluetooth. Not a mysterious or involved word but just a way of describing 'a short-range wireless technology standard that is used for exchanging data between fixed and mobile devices over short distances' (wiki)
With audio equipment at home which does not have Bluetooth built in (which allows for the use of wireless headphones) I expected I would have to pay out several hundred for such a radio / CD player with it. Not the case. By obtaining a 'Bluetooth Wireless Audio Transmitter and Receiver' a small thing you plug into an existing earphone socket on your equipment you've done what you need to do for just around £80. All you need to do then is purchase the wireless headphones. Getting the transmitter to 'talk' to the headphones is easy (they call it 'pairing') but any problems then some young person will have no trouble helping you out.
I would like to express my thanks to the Richer Sounds branch in Cheltenham and manager Jason who assisted me. Researching and sourcing what you need is only the half of it. You need someone in the trade who can assure you that what you have in mind will work.