first - I do not think you will find a working cd reader for 50 GBP. Maybe "not tested" - probably with the same problem.
second - you have to check part number of your reader first, you have to buy reader with the same software level (I can check by part number if you do not know software version).
you can enter radio code "blind" not only with steering control but also with radio buttons (not on cabasse cd changer).
1st digit with button 1, 2nd digit with button 2, 3rd digit with button 3, 4th digit with button 4. you have 0000 on the start, each press increases by 1.
confirm is done by long pressing of button 6.
and returning to previous question.
It can be a little hard to visit me but possible if you plan to make a trip to Poland
I can sell you reader (tested and working) + latest UK map for 120 GBP (with express shipping via GLS - european parcelforce partner).
you can pay after testing, via paypal or bank transfer.
But I need your reader part number first.