Greetings! This is an interesting question, and one which concerns a fair bit about the experience of British colonial troops during the 1800s (as well as the overall nature of the British imperial troops of the Empire). I am unfortunately unable to provide primary accounts from troops of the time period who were deployed in India or Africa, but I can provide a general "overview" of the situation regarding the service in those two areas from about 1830-1900. Let's begin.

The General Picture

Not an exhaustive description, but one which helps to set the scene.

Contrary to what some pop-history sources may lead one to believe, the deployments of the British Army in the early 1800s was not the centralised or concentrated spread of contingents throughout the Empire. Instead, it was formed of "penny-packets" consisting of only a few thousand troops and officers across the various stations of the Empire. Almost two-thirds of the British troops were stationed in the home isles, in the event of European war which would require their hasty deployment. Life in these garrisons was relatively peacefully (though of course was dependent on the station and its political nature). A troop's duties would mainly consist of drill and patrol of local settlements, as well as being dispatched to act like a 'local police force' in areas where a professional constabulary was not available. Active duties in these garrisons were very long, often in the period of years or even a life's service in the military, to ensure a constant (if at times illusory) armed British presence in the colonies.

In the white-settler dominions, namely Canada, Australia, and New Zealand (we shall get onto South Africa as a special case later on), the late 1800s saw the establishment of the colonial militias, usually formed of an Active Army (or Active Militia) and Reserve Militia (untrained and unarmed men). The service for the Active Militia in Canada was three years, with an annual training period of eight to sixteen days. Volunteer forces often made up the garrisons elsewhere, though almost always supervised by British Army officers and commanders.

India - The EIC and the British Army

The British Army in India was a different case altogether. Militarily, the British in India up until 1857 were represented by the three presidency armies of the British East India Company: the Madras Army, Bengal Army, and Bombay Army. In 1840 the Company had an army of 250,000 men (the largest and most modern in Asia), mostly formed of troops from across the subcontinent (collectively referred to as sepoys) and commanded entirely by European officers (until the late 1800s, when reluctant efforts were made to expand the officer corps to include local persons). Further, the EIC also paid the government in London to "lease out" a portion of the actual British Army; in 1840 this contingent was 20,000 men strong (and grew to 30,000 by 1847).

Common duties in the company's army often included the usual drill and patrol of the company's assets/infrastructure, whilst often assisting in law enforcement across the territories, as well as the odd border skirmish or larger expansion effort into parts of India which were not in the company's possession. Duties in the army, especially for the sepoys, were often for years and life, though the European officers were not obligated to stay on for as long as they lived.

It was only after the Sepoy Mutiny of 1857 and the transfer of control of India from the Company to the British government that the decision was made to reduce this army greatly: the British garrison was increased to three times its-pre mutiny strength, whilst the sepoys were reduced by half. From 1860 onwards, the ratio of British soldier to Indian was always 1:2, and at times nearly half the entire British Army was kept on station in Indian cantonments. There they would assist in quelling any signs of mutiny, taking part in border conflicts, such as the two failed invasions of Afghanistan (1838-42 and 1878-80), patrolling local settlements, and acting like an armed police force where called upon.

South Africa

I have written more on the curious nature of British imperialism in the 1800s in South Africa here, so consider going there for some foundational knowledge on the presence of armed forces under the Union Jack.

The British Army in South Africa was perhaps one of the most dangerous assignments for a fresh soldier in the 1800s. Ignoring for even a moment the terrible weather conditions, potentially-fatal sicknesses, and general lack of access to proper medical care, the South African veld (its bush landscape) was full of opponents. In these areas, the British had to constantly face off against Boer voortrekkers who were masters of early guerilla warfare, and the local tribes such as the Nguni and Xhosa (whose resiliency in recovering meant that entire villages had to be burned and all livestock killed). Duties here often consisted of repelling constant raids on supply depots, army barracks, police posts, and convoys. Alongside those more regular duties, you could be called upon to take part in reprisals against an armed tribe or settlements, or to conduct "sweeps" of the veld to root out any enemies (most prominently, the experienced and highly dangerous Boer Kommandos).

As such, duties in the South African army contingents stretched into years and decades (and that does not take into account the larger conflicts you might have been called up to fight in, such as the wars against the Ashanti or the Zulu and Boer Wars of the late 1800s). In the later years, your force would be supplemented by locally-recruited native battalions or irregulars (a particular favourite tactic of 1800s British imperial commanders was to send the natives into the bush first, sweeping for enemy presence before the British troops set foot).

Hopefully this general overview helps, and feel free to ask any follow-ups on the British colonial soldiers' role in the 19th century as you see fit.

Sources

Darwin, John. The Empire Project: The Rise and Fall of the British World System 1830-1970. Cambridge: Cambridge University Press, 2009.

Darwin, John. Unfinished Empire: The Global Expansion of Britain. New York: Bloomsbury Press, 2009.

Jackson, Ashley. The British Empire: A Very Short Introduction. Oxford: Oxford University Press, 2013.

Miall, Stephen. "Military Service in the Colonies." Journal of the Society of Comparative Legislation 2, no. 3 (1900): 440-45. Accessed February 18, 2021. http://www.jstor.org/stable/751988.

Moyse-Bartlett, H. "THE BRITISH ARMY IN 1850." Journal of the Society for Army Historical Research 52, no. 212 (1974): 221-37. Accessed February 18, 2021. http://www.jstor.org/stable/44223869.

Spiers, Edward M. The Victorian Soldier in Africa. Manchester; New York: Manchester University Press, 2004. Accessed February 18, 2021. http://www.jstor.org/stable/j.ctt155jj67.