The British Empire was a empire that existed from the 1600's (as in OTL) until (in this timeline) the Anglo Federation was formed on June 12th 1979. The empire once stretched from mainland Britain to New Zealand (with claims stretching across the world, even the Antarctic (no Antarctic treaty in this timeline). This is only a summary (important parts) of it's history as it's to long to give a full timeline. So, without further ado, let's begin.
Formation & Rise (1600's/1700's)
The british empire began in the early when an unknown British sailor made a port in modern day Newfoundland (St. John's area). The economic benefits of the colony (fish etc.) cause the British to expand down the coast (just as in our timeline). By 1700 the British and Spanish are the only powers in North America (France focuses on other places and never settles Canada in this timeline). While the early 1700's saw co-operation between British and Spanish (even the British buying Texas for 150,000 pounds in 1725, which was a lot at the time). English culture was spreading through North America. However, the northern portions of New Spain (even outside of purchased Texas) were becoming more English than Spanish. In the mid 1700's tensions began to arise in Alta California where thousands of British settlers outnumbered the Spanish settlers around 3-1. Things were set for a war in the New World.
North American War (1748-1760)
The Spanish ransacked a British horse-and-buggy that was delivering goods to a small town on the border of Texas and New Spain. The British Empire made an official declaration of war as soon as news got back. The Spanish Empire mobilized and their armies went from a mere few thousand to over 50,000 men. The British Empire had a total of 85,500 men. Of course. British blockades of the Spanish homeland were made, do to British naval superiority, which meant New Spain would have to rely on it's own troops. The British invaded New Spain and took it's capital (also called New Spain) in 5 days. New Spain's armies were obliterated by 1750. The Treaty of Madrid was signed on June 13th 1760. The Treaty gave Britain Alta California.
The American Revolution is almost as in our timeline with the exception of a larger rebellion, swifter peace and America stretching from the East Coast to the West Coast. This means in the future Manifest Destiny is not made an ideology, as there is no need for it. The British cannot handle this much land rebelling and just give up after a few weeks. Texas rebels separately and becomes the Republic of Texas on February 2nd 1777 (an actual nation, not like it's non-official successor during the 1920's). Texas purchases or "occupies" -despite not being at war with Spain- Bordering regions they want such as the El Paso area and the modern Texan part of the Rio Grande). The US wants Texas to join them, but Texas repeatedly refuses (cultural and royalty differences). The US mobilizes at the border and asks one last time, but Texas says it'll fight for it's independence.
Texan War of Independence (1791-1807)
The US declares war and invades eastern Texas. The British ask Texas if they intervene if it'll become a "Dominion" (a colony with self-governance) until 1850, at which time they'll become sovereign again (as a British ally of course). Texas can't refuse and agrees. The British invade the US through Canada. the British swiftly take most of New England until they are halted at the Battle of Boston (which lasts over a month). In Texas, America withdraws and begins focusing on British Canada. This allows Texas's forces (who were forced to retreat to western Texas) to retake the east and invade the Southern US. Southerners in Louisiana support Texas and a small rebellion begins in Louisiana. The US, well bitter about it, accept a peace treaty on February 13th 1807. Texas is made a Dominion and the US will not arm bordering regions of Texas or Canada. The British will gain Caribou.
Becoming a great power and the empire's "peak" (1800's)
The British were the greatest power of the 1800's and the empire stretched around the world. The British owned the whole guangxi (a former region of China) which included Hong Kong, the British name it British China. Macau is bought by Britain for 75,000 pounds; this makes British China "united". The Empire annexes the Maori people of New Zealand by 1850. Texas also became fully independent in 1850. Texas would keep good relations until it's collapse in 1880. Tensions with Boers in South Africa soon cause a war (or multiple wars depending on who you ask).
The Boer War(s) (1855-1900)
The Boer people of South Africa wanted independence, which of course the British denied. The First Boer rebellion begins, however is quickly snuffed out. This angers all Boers who band together and begin a huge rebellion, wanting South Africa to go back to the Netherlands. Tens of thousands of Boer men begin engaging the British forces (who are only ~1-2 thousand men). The British progressively defeat the Boers time and time again and finally force the Boers to accept British rule. The Boer people start organising a second rising and it begins in 1862. This rebellion kills many more Boers as the Boers fight to the death to try and defeat the British. This would be the last major rebellion, although smaller rebellions continued until the turn of the 20th century. Boer culture would fade and die out by 1920. Afrikaans never becomes a language.
The Dominions (1860's/1870's-1933)
The British made the first Dominion (the Dominion of Canada) in 1867. This was followed by the Commonwealth of Australia, The Dominion of New Zealand and the Raj (the final Dominion created in 1875 and initially still called British India). Guangxi is proposed as a dominion but is never made an official Dominion and never self-governs. This Dominion era is almost universally accepted to have ended in 1933 when the Statute of Westminster passed. The Boer war was the cause of Dominions as the British feared these nations would also rebel if they had no say in anything.
The Alyeska Border War (1868-1871)
The border between Canada and Alyeska had been under dispute for a long time, the British and Canadians claimed the border was only north of the Panhandle while Russians and the Alyeska people claimed the Panhandle and (to a lesser extent) B.C in it's entirety. Tensions boiled over when Alyeska and Russian people settled Vancouver Island. The British declared war. The war would be the most humiliating loss for the British in history, as they lost B.C.
Irish Rebellion of 1870
The largest rebellion in Irish history (even larger than the Easter Rising) began in 1870. All of OTL Republic of Ireland (and parts of OTL Northern Ireland, although reluctantly) rebelled against the British. Like the Boer people the Irish had a long history, although most of their history was under Britain. Ireland had never liked this and the Irish always hated British rule do to cultural and religious history. The Irish collectively decided to rebel. The Irish were initially successful, but soon the British began to fight back with the Royal Army, which had over 100,000 men. The Irish had an untrained militia of just 25,000. The Irish sued for peace just 8 months after the rebellion began. The Treaty of Dublin was signed and stated the Irish must pay over 10,000 pounds in damages.
The World Wars and rapid decline of the Empire (1914-1945)
The World Wars destroyed the empire. Ireland became independent (in the Dublin region) in 1916 with the Easter Rising. In WW2 Hitler's bombing of London and the detection by Hitler that the British had cracked Enigma led to the Americans having to intervene to keep the British from a surrender. The Guangxi province and the port cities of Hong Kong and Macau are occupied by the Japanese. The Raj rebelled in 1943 and became independent later that year. The Raj collapsed in 1951 into the nations we see today. The Dominions became independent in between the wars with the Treaty of Westminster although the royal family temporarily fled to Canada when Britain looked close to collapse.
Post-WW2, the Cold War and end of the UK and it's Empire (1946-1979)
This was the last era of the UK as it would soon join the Anglo Federation in 1979. But in it's final years the Empire did good, for instance it reformed policies and rebuilt after WW2. Regions like South Africa (although completely english cultured) gained independence peacefully and Ireland gained all of Ireland (including the North). Guangxi (including the port cities) is given back to the Chinese (PRC) (although America supervised the handing-over) in 1960. The Empire's final years consisted of anti-communist ideas and it's end. The mainland and few remaining small island colonies joined the Anglo Federation along with Canada and the founding nation of the US. Newfoundland initially becomes independent, but joins the Federation soon after.