An SCT controller described possible conflict event after failing to insure visual approach clearance was issued to a MYF arrival who flew through the final course and became traffic for a SAN air carrier arrival.

Narrative

Aircraft X was cleared for the visual approach to MYF airport. It's possible that I didn't clear him or that he didn't read back the clearance. I transferred communication to MYF Tower when he was approximately twelve miles from the airport. Air Carrier Y was cleared for the localizer Runway 27 approach to SAN. I transferred communication to SAN Tower when he was approximately twelve miles from the airport. Aircraft X went through the MYF final; which put him on a converging course with Air Carrier Y. I noticed this and called MYF Tower and told them to immediately turn Aircraft X to a 300 heading and maintain 4000. They did not do this. I don't know why. I called SAN Tower and told them to turn Air Carrier Y immediately to 240 and maintain 4000. Their response was to ask me why. I told them for traffic. I called back MYF Tower; because I noticed that Aircraft X wasn't turning. I told them again to turn him immediately. Approximately one minute after I told SAN Tower to turn Air Carrier Y; Air Carrier Y started a turn to the southwest. Approximately two minutes after I told MYF Tower to turn Aircraft X to the northwest; Aircraft X started a turn. At this point; I believe they were still separated by three NM. Both Towers said that they could 'barely hear me.' I'd had no such complaints that I can recall in at least the previous year. Recommendations: make sure I clear a guy for the visual and that he reads it back. Train Tower Controllers that when a RADAR Controller instructs them to relay a control instruction to an IFR aircraft that time is of the essence; especially if the word 'immediately' is included in the instruction. Find out if there's a problem with the landlines or other equipment that would result in both Towers able to only 'barely hear' me.