Some of the brands of alcohol which quenched the thirst of the British Empire are with us still.

Gin was one of the favorite drinks, especially Gin and Tonic. The tonic was made with quinine and thought to help prevent or alleviate malaria in tropical regions. Tonic did not taste so good on its own, but mixed with Gin, the Gin and Tonic became the preferred drink of British Imperialists in warmer climates.

The Gin Brands of the British Empire that are still with us today are:

Beefeater: 1820

Boodles: 1845

Booths: 1740

Gordon’s: 1769

Plymouth: 1793

Tanqueray: 1830

Beer:

The best known beer brand in the British Empire was Bass, founded in 1777. The Bass red triangle became Britain’s first registered trademark. Bass were the first to make “India Pale Ale” a very hoppy beer which (thanks to the hops) kept well enough to be shipped to India.

Scotch was not widely drunk in the British Empire until the last half of the 19th century. Popular brands included:

Johnnie Walker - John Walker made and sold Whisky from 1820, but it was not until after blended Scotch became legal in 1860 that Whisky really started to expand as a drink, and Walkers whisky would not have been generally found around the Empire until the 1870s at the earliest. It was called "Walker's Kilmarnock Whisky" until 1908, when it was re-branded "Johnnie Walker".

Other Scotch whisky brands which are still with us and were popular in the Empire in the late 1800s were often founded much earlier, but Scotch was not exported heavily until the 1870s or 1880s, after blended whisky became legal. Some of these brands were:

Justerini & Brooks

Chivas

Ballantine

Rum, which was the drink that floated the Royal Navy when it dominated the oceans of the world, was bought by the cask by the Navy from the West Indies, and not generally branded.

Pussers Rum. made in Tortola in the British Virgin Islands claims to be made based on research into the specifications laid down by the Admiralty for Rum which they purchased for the Rum ration. How uniform Royal navy Rum was in the 19th century, is dubious.

The two most distinct beverages from the British imperial period that are commonly enjoyed today would be Gin and Tonic and IPA's (India Pale Ales). Both are directly linked to Britain's imperial endeavours in India, although most of the common origin story of the IPA is a myth. The Bow Brewery, frequently credited with developing the IPA, went out of business in 1927, but IPA's with recipes from the 19th century are available, especially in the UK. Porter and several other styles of Ale, were also developed in the British Isles during the 17th-19th centuries. Guinness Extra Stout is technically a porter, although it isn't marketed as one. Bass Brewery, founded in 1777 and famous for its Pale Ale, was one of the largest breweries in the world in the late 19th century, although it is now owned by Imbev.

Gin and Tonic, of course, was developed as a way to make the bitter tonic water the soldiers in India needed to drink to avoid malaria more palatable. Since the soldiers were already given gin, the resulting mixture was inevitable. The drink would have originally contained much more quinine in the tonic water, and as a result would also have required sugar. Modern tonic water has less quinine and is often slightly sweetened. Limes, or whatever citrus was available, have also been a part of the recipe since the beginning. Beefeater and Tanqueray are both gins dating from the imperial period.

Rum would have been made, traded, and consumed by the British Empire, but rum recipes date into antiquity.

Britain's climate is not great for vineyards. Wine and Brandy would have been available, but mostly imported from continental Europe and perhaps out of the common man's price range. Ciders would have been more readily available. Westons and H. P. Bulmers have both been making cider in Herefordshire since the late 19th century. Strongbow is one of H. P. Bulmers more modern styles.

Whiskey predates the British Empire, but would have been a common and important spirit in the British Empire. Bushmills, an Irish whiskey, has been open since 1608. Jameson has been running since 1780. Irish Whiskey and Scotch were somewhat important exports for Ireland and Scotland. Whiskey was also an important part of Canada and the American colonies' economies. There are numerous Whiskies available from 17th-19th century.

Gin - absolutely gin, especially in Africa and Southern Africa. /u/mormengil has provided a very excellent list of various alcoholic drinks of the British empire already, but in particular Gordon's, Hendricks, and Tanqueray were the drinks of choice for the colonialists in British Africa. Gin was so heavily identified with the British industrial imperialism of the 1880s and 1890s in the Transvaal that gin was even used as an enticement to get workers for the mining operations around Johannesburg. In this case it was simply a cheap, locally distilled spirit (rather than imported English gin) which workers could be rewarded with (out of their own pocket of course) after a week of work, and was aimed at both the poorer white settlers as well as Africans.

However, advertising campaigns in turn of the century colonial Zimbabwe (particularly in white Salisbury) took a different tack, emphasising the 'Britishness' of London gin and the health benefits of gin and tonic as much as the middle-class lifestyle that went with such consumption. The concept of 'sundowners on the veranda' was heavily peddled by various gin distilleries, both domestic and British, as a way of recapturing the fictional 'glorious' age of settler society, and used the heritage of the British empire (gin and tonics amongst British officers in India, or the Pioneer Column of 1890) as something for white settlers to buy into. Often tied to the lifestyle of affluent whites in Cape Town, gin and tonic was represented, if not in reality, as an inherent aspect of the British colonial culture in Africa, as much as horse-racing or cricket; civilisation in the savage hinterlands was dependent upon the transplantation and syncretism of perceived British cultural traits into a new white settler society, and gin and tonics provided an element of 'Britishness' in a scary new world. Gin, after all, had been the drink of choice in England during the eighteenth century.

Even up to the 1960s and beyond when the British Empire was being rapidly dismantled colony by colony, white Rhodesians regarded the gin and tonic as a fundamental aspect of their white imperial culture, a legacy of their settlement during the colonial encroachment of the late-19th century. Read any of the many memoirs or autobiographies of white Africans in former British colonies and gin and tonic remains a staple part of many social recollections; drinks on the deck meant gin and tonics or local (white-brewed) beers. Certainly, even during the sanctions of the 1960s and 1970s, many white Rhodesians 'ran the blockades' to South Africa, bringing back the priorities like food, petrol and Gordon's or Hendricks gin.

The real question, however, is to what extent this is imagined significance on the part of a consistently challenged identity of a white settler culture, or whether it was a genuine aspect of British imperialism in Africa. Was the imperial history of gin simply used as a marketing tool, designed to appeal to the innate belief in superiority that was commonly perceived as being inherent to all white colonials in the British colonies, most often after the fact? I cannot, off the top of my head, think of any academic sources that have addressed such a question, but perhaps others can. The knowledge above comes from bits and pieces in many, many different sources. If there is one bit that is of particular interest, please ask away and I shall try to dig out where its from.

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