The New Breed, Part 1 North Africa colour and markings series by Dennis Oliver and Michael Starmer: On 23 October 1942, Sherman III tanks accounted for approximately 30 vehicles out of the 252 Shermans equipping operational unids.
Also according to this book, 24th Armoured Brigade (ex 8th armoured division, not 10th armoured division, but retaining 8th armoured divisional sign), had the first Sherman III’s. Large names were painted onto the rear hull of these vehicles. 41st (Oldham) RTR exaples are Coyote and Cocky. Cocky was the battalions first cassualty, but was repaired, and was apparantly handed over to the 4th (light) armoured brigade, whith whoom it went into action again, and was knocked out again.
When the first replasement tanks arived, most were Sherman III’s, and when the Tunesian campaign started, most Sherman’s were Sherman III’s.
So, concluding, as far as I know, 24th armoured brigade, led the first Sherman III’s into action at El Alamein. It may have been that some other unids had Sherman III’s also at the time, but none are mentioned as far as I’m aware. But yes, some were used at El Alamein, and a lot in the closing phase of the Africa campaign and the Tunesian campaign.
Cheers,
Joppe