This is the British army "Service Dress" as worn during World War I and in the inter-war period. This to me looks like post WWI, just on the basis of the front man's haircut and the lack of mustaches. Mustaches were actually compulsory at the beginning of WWI, I think that regulation was dropped in 1916 so that would be the earliest date.

As to branch, artillerymen definitely wore lanyards like that, but so did a lot of regiments. These look like draft horses not riding which might point to artillery again.