Radio 4 Extra is only available on digital, so if you do not have a digital radio you can not listen to it. Only a few upmarket cars come with digital radio.
I have a digital radio but use it relatively little, the problem is we have quite a big house and I usually carry the radio from room to room when I am listening, depending what I am doing, and I find that digital radio reception, like FM reception is not reliable and if the radio is put down on the 'wrong' side of the room or in a room at the front of the house reception is very poor. Whereas my little analogue radio that can receive long wave gives me a reliable signal no matter which room I am in or where in the room I put the radio.
I also find that although my digital radio is meant to work on mains or batteries, it does not work well on batteries and when I got in contact with the manufacturer's helpline they were absolutely gobsmacked that I should want to run my radio on batteries.
DH is quite put out. It was quite an expensive radio and he bought it for me as a Christmas present so that I would be able to listen to the extra programmes as I wandered round the house. In fact it lives in the kitchen plugged into the mains in the one place I can get reasonable reception.