Just want to put in a good word for Cruz Classic Radio in California (www.cruzclassicradio.com). They repaired the non-functioning BMCD radio on my 1963 E-Type and replaced all the old capacitors. They also upgraded the radio with added circuitry (but no visible alterations) so it can connect to my iPhone (by hard wire or Bluetooth) to play FM stations or stored tunes.
Communication with them was outstanding, the price was reasonable and the results were excellent.
Their website indicates an emphasis on American radios, but they now feel comfortable with E-Type radios as well. Besides, the head man, Jeremy, seems to have an British accent, which I suspect is a huge advantage when repairing anything on a Jaguar (firstname.lastname@example.org).
Technical advice Q&A