Thanks tonepad.
Whittling down the possible regiments based on cap badge rules out the Wiltshire Yeomanry, 12th Royal Lancers, and the Australian Light Horse.
A first google for "wwi postings regiment name" with the remaining regiment names comes up with the following (I've omitted the information on the Yeomanty units that didn't go overseas)
https://www.longlongtrail.co.uk/army/regiments-and-corps/the-british-yeomanry-regiments-of-1914-1918/pembroke-yeomanry-castlemartin/Only 1/1st Pembroke (Castlemartin) Yeomanry were posted overseas
Pre March 1916 UK (November 1915 : dismounted)
March 1916 : moved to Egypt. On arrival the brigade merged with Welsh Border Mounted Brigade and formed the 4th Dismounted Brigade.
2 February 1917 : merged with 1/1st Glamorgan Yeomanry to form the 24th (Pembroke & Glamorgan Yeomanry) Battalion, the Welsh Regiment and came under orders of 231st Brigade in 74th (Yeomanry ) Division.
Moved to France in May 1918.
https://www.longlongtrail.co.uk/army/regiments-and-corps/the-british-yeomanry-regiments-of-1914-1918/glamorgan-yeomanry/Only 1/1st Glamorgan Yeomanry were posted overseas
Pre March 1916 UK (November 1915 : dismounted)
March 1916 : moved to Egypt and formed 4th Dismounted Brigade with the Welsh Border Mounted Brigade.
2 February 1917 : merged with 1/1st Pembroke Yeomanry to form the 24th (Pembroke & Glamorgan Yeomanry) Bn, the Welsh Regiment and came under orders of 231st Brigade in 74th (Yeomanry ) Division. Moved to France in May 1918.
https://www.longlongtrail.co.uk/army/regiments-and-corps/the-british-yeomanry-regiments-of-1914-1918/denbighshire-yeomanry-hussars/Only 1/1st Denbighshire Yeomanry (Hussars) were posted overseas
Pre March 1916 UK
March 1916 : moved to Egypt and formed 4th Dismounted Brigade with the South Wales Mounted Brigade.
February 1917 : formed the 24th (Denbighshire Yeomanry) Bn, the Royal Welsh Fusiliers and came under orders of 231st Brigade in 74th (Yeomanry) Division. Moved to France.
https://www.nam.ac.uk/explore/10th-royal-hussars-prince-wales-own10th Royal Hussars
The 10th deployed to the Western Front in September 1914,
remaining there throughout the First World War (1914-18) with 3rd Cavalry Division.
It fought in many battles including Ypres (1914 and 1915), Loos (1915), Arras (1917) and Amiens (1918).
(and from
thelonglongtrail)
10th (Prince of Wales’s Own Royal) Hussars
August 1914 : at Potchefstroom in South Africa. Recalled to England and joined 6th Cavalry Brigade in 3rd Cavalry Division at Ludgershall.
8 October 1914 : landed at Ostende.
20 November 1914 : transferred to 8th Cavalry Brigade in same Division.
12 March 1918 : transferred to 6th Cavalry Brigade in same Division.
https://www.nam.ac.uk/explore/3rd-dragoon-guards-prince-waless3rd Dragoon Guards
The 3rd Dragoon Guards arrived on the Western Front in October 1914.
It remained there for the entire First World War (1914-18),
taking part in many engagements including the first and second battles of Ypres (1914 and 1915), Loos (1915), Arras (1917), Cambrai (1917), St Quentin (1918) and Amiens (1918).
(a lot more detail at
thelonglongtrail)
So it looks like the UK, Egypt or France.