India: there were 52 British infantry battalions and 9 cavalry regiments forming the British Army in India. (Which was separate to the Indian Armies - Northern and Southern). It's true that these weren't formally organised into divisions until August, but they were Regular troops already under arms in January 1914. They became the 8th and 27-29th Divisions once war broke out. To simplify, I gave them those numbers straight away.
South Africa: The Databook says there were 4 infantry battalions and 2 cavalry regiments garrisoned here. I simply took that to be roughly half a division's worth of troops, and (anachronistically) gave it the name of the first South African division to be formed. I think that giving a 30 strength division is better than three separate 10 strength ones, although I'm happy to go with your thoughts on the names. But where do you get an entire extra cavalry division (12 regiments) from?
The Territorials: I didn't forget them, I deliberately left them out.

These were
not combat units available for use in early 1914. They were purely administrative units, used for training part-time volunteer soldiers (who spent two weeks per year with the army, the rest doing a civilian job), and by law they couldn't even be sent outside the country! When war broke out the Government decided to ignore the Territorial Force and organise a new army from scratch; soldiers from the TF units were encouraged to volunteer for the new divisions. In short, the only infantry available to Britain for service in Europe in January 1914 were the six Regular Army divisions and the colonial garrisons.
Unit Strengths: I worked out the actual strength based on one battalion = 8.33 strength points, rounded off to the nearest ten, and ignoring anything less than 25 strength points in an area (or, in some cases, combining garrisons from several provinces into a single larger division). If a garrison was made up of several different units, I chose one to give its name to the entire force (for example, Malta's garrison included 5 battalions from different regiments, but because the Databook says the London Regiment contributed most sub-units during the war, I just called the unit "London Regiment"). Because places like Singapore only had a couple of battalions stationed there (= 16 strength) I left them out completely.
Some questions: Where does the New Zealand Division come from? AFAIK NZ's troops were incorporated into the ANZAC Division formed in January 1915, and they didn't have a division of their own until 1916.
'Gough's force' - the Second Cavalry Division. According to
this site Britain had 5 cavalry brigades before the war, of which the 1st to 4th made up the 1st Cavalry Division. So if you want to assign a unit for the fifth, it should only have a strength of 25. Also, the 5th Brigade was stationed in York (province 488)