Jaguar XJ the car radio

Have you tried rescanning the stations ? Cant see why the radio cant be replaced , plenty of car audio centres that should advice on options .
Can check if this applies to your radio but varies from set to set

Auto memory (A-MEM)

The automatic memory function programs the nine strongest stations on the selected waveband into presets 1 to 9. To activate this function, hold the A-MEM button for at least two seconds.

The radio is muted briefly while it searches the waveband for the nine strongest stations. A beep indicates that programming is complete and preset number '1' is selected. If stations cannot be found for all preset buttons, those found will be allocated to preset buttons, starting with number ‘1’, leaving the remainder not programmed. The display will show 'NO FM' or 'NO AM' if unprogrammed buttons are selected. To switch between the A-MEM preset stations and your own presets, press the button for less than two seconds. A-MEM with radio broadcast data system (RBDS) selected if the A-MEM function is operated while in RBDS mode, the radio will be muted briefly, while a search is made for the nine strongest RBDS stations. Similarly, if A-MEM is used with Traffic Announcement (TA) activated, the radio will only program the nine strongest RBDS stations carrying traffic information. If stations cannot be found for all preset buttons, those which are found will be allocated to preset buttons, starting with number ‘1’, leaving the remainder not programmed. The display will show 'NO FM' or 'NO AM' if unprogrammed buttons are selected.

Note: When used correctly, RBDS and TP are very effective additional features in the radio’s capabilities. However, if these facilities are used without full understanding, they may cause a situation confusing to the operator. This is less likely to occur as more RBDS stations become available."