Answer: I have looked at literacy although more in terms of soldiers’ ability to write and read letters home and there’s quite a bit of work on this – have you read Jonathan Rose’s The Intellectual Life of the British Working Classes? That has interesting material on reading in the era of WW1. People like Paul Fussell and Samuel Hynes have argued that it was a ‘literary war’ – and their bibliographies might be helpful if you haven’t already used them, but it’s evident from some soldier’s experiences that reading didn’t come that easily to all, e.g. Stephen Graham comments on this in his memoir A Private in the Guards.
There’s also this database that the OU have set up (http://www.open.ac.uk/Arts/RED/):
The UK Reading Experience Database (UK RED) is an open access database and research project housed in the English Department of the Open University. It is the largest resource recording the experiences of readers of its kind anywhere. UK RED has amassed over 30,000 records of reading experiences of British subjects, both at home and abroad, and of visitors to the British Isles, between 1450 and 1945. These include both famous and anonymous readers.
I’m not sure how searchable it is now – last time I looked the answer was ‘not very’ but that was a few years ago and it was something that they were working on.
It might be worth searching the IWM online collections if you haven’t already done so – I did a quick one for ‘reading’ in WW1 and got a lot of hits, but it would mean having to trawl through and see what’s useful.