Two candidates from medal records, one was a Waterways and Railways man (in his case railways)the other had been discharged to the category that covered men who were of more value to the country than the armed forces (such as miners). No personal info for either though!
Perhaps ask the RE Museum
http://www.re-museum.co.uk/ whether they recognise the term which doesn't ring a bell at the National Archives or Imperial War Museum etc etc
There's no possibility I suppose that the "Hill" is a badly written abbreviation for Territorial??
MaxD