Thanks for the other pages of the letter, I must admit I was wondering how Col Harding came to be writing in the same letter. The letter as a whole indicates a fairly close relationship between Mrs Nuttall and the men of the Field Ambulance. Perhaps she had some connection with them in the early years of the war. Although there are other people referred to rather cryptically (the twins, our Bungalow friends) I'm not sure this is going help identify them. From Pte Palmer's service details which you provided it looks as though once they were deployed on operations they were just referred to as 2/2 London Field Ambulance without the LofC bit. The Long Long Trail website says this unit served initially with the 58th (2/1st) London Division until February 1916 and then with 56th (London) Division until the Armistice.
According to
Wikipedia 58 Div spent most of the first three years of the war in reserve in the UK, significantly in the Ipswich area for part of that time:
Training.
In August 1915, the division concentrated around Ipswich in Eastern England and received the number 58, its brigades being numbered 173–5. Here it formed part of First Army in Central Force. In September 1915 the 1st Line artillery brigades went to France and were replaced by the division's own 2nd Line units. In the Spring of 1916 the division took over a sector of the East Coast defences. Then in July 1916 it went to Sutton Veny on Salisbury Plain for final training before deploying overseas. [...] The division began embarking for France on 20 January 1917 and had concentrated by 8 February. It then served for the remainder of the war on the Western Front.
Clearly from the letter, which is dated 2 April 1917, the Field Ambulance is in France somewhere and is by now part of 56 Infantry Division.
The Long, Long Trail has a useful article about the 56th Division and the actions in which it was involved, here:
https://www.longlongtrail.co.uk/army/order-of-battle-of-divisions/56th-1st-london-division/My guess is that 2/2 London Field Ambulance would have been acting in direct support of one of the Brigades (167, 168 or 169) although without seeing any of the operation orders for the various battles I wouldn't want to guess which. If that information does come to light it should be possible to narrow down more precisely where on the battlefield Pte Palmer met his death. If you would like to follow up on this particular aspect, search the TNA website for the war diaries of those three brigades. Most of them have been photographed but are not digitized, so you will need to download them (for free, once you have registered with TNA) and then do your best to stumble through the often tiny handwriting and copious military jargon in the hope of of seeing a reference to 2/2 Field Ambulance. The most likely place within the diaries will be if they included a copy of an operation order (OpO) for a particular phase of the battle. The good news is that, if there is an OpO, it will have been typed and so be easier to read. You will probably need to scroll towards the end of any OpO to where they talk about supporting troops. However if there had been no change to the previous order of battle, it is less likely anything will be noted about the medical support.
