Hi Joanna and Martin
TNA reference: WO 95/4359 Lines of Communication, Embarkation Officer (Mudros). As far as I'm aware it isn't available on line. I have photographed the file, about 50 sheets, if that can be of any help.
Martin, there are seveal references to 9th Worcesters on 11th, 13th, 14th July 1915. There are quite a few mentions of reinforcements to 29th Division without the specifics of which Regiment it refers to. The first mention I can find for 4th Worcestershire Regiment is Saturday 18th September 1915 as attached below (I have had to crop the page due the 100KB limit). The only other specific entry for 4th Worcester is on 5th January 1916: 'CALEDONIA
sailed for Alexandria today with ......4th Worcesters, and Various Details, of Artillery.'
There are no hospital ships mentioned after14th July until 8th August when DEVANHA
arrived (no mention of where from). I believe it took around [11 hours]* to get to Mudros from Suvla. Prior to 14th July; on 7th July ASTURIAS
arrived and on 6th August GLOUCESTER CASTLE
arrived both from Malta which suggests that they were heading for the peninsula.