Son of S-Type Driver

Hi All First time poster here. My father has a much loved S-type, 2005 build, purchased 2007. 2.5ltr Auto About two years ago (c50k miles) on a hot summer drive in southern England it flashed up 'gearbox fault' when crawling through start stop traffic, and trying to change gears at low speed. With the error message up, the car could not change gear. This problem has persisted intermittently ever since. Vehicle now at 57k. Specialist mechanic recently changed oil and filter in order to fix the problem. After a couple of hundred miles, it recurred, again while crawling in start/stop traffic. In all cases, turning the engine off for about 10-20 second seems to clear the fault. For a while before the problem emerged, changes were sometimes a bit jolty in low gears changes, they still are a bit juddery at times (but equally a few moments later at the next set of traffic lights, can be as smooth as anything. The mechanic said if oil change does not work, a new gearbox is needed. I am not fully convinced the problem is mechanical - turning the engine off and back on again seems to sort the error out, it only happens at slow stop/start conditions and in hot or cold temperatures. What other issues, short of a mechanical fault, could be the problem here? And are there any gearbox expert mechanics in the London area. My father seems to think one of the error codes was P1 or something similar (this is probably not very helpful). Thanks Mike