The P.O.D. is in the 1660s with a more successfull war against the Dutch, instead of swaping New Amsterdam for territory in Guyana, New Amsterdam
is taken and no territory is given to the Dutch at all. In the 1760s the British do better against Spanish in that war and instead of returning the Phillipines at the peace they decide to keep it. With the additional Spanish maps now available New Guinea is taken in the 1790s to secure the northern approaches to NSW.
After the battle of Bunker Hill the British government authorises the British Commander in America to concede to American demands and a truce is called. Attempts by the New Yorkers in the Continental Congress to push
for direct representation in the British Parliament cause a resumtion of hostilities in 1777 when the southern members realise this would result in
the automatic end of slavery.
The new revolutionary war only involves the southern colonies with George Washington returning home to consider his view of slavery. The Dutch, French and Spanish involve themselves in this war and the war spreads
to Africa, India the Mediterean and the West Indies as in OTL. An American army of Northern Loyalists and Patriots invades the south, this army has British regular troops but no Germans.
The Southern Patriots don't have as much support as in OTL because the only issue of liberty involved is those in slavery. Southern Loyalists have
an easier time as well and they free and arm slaves to increas their numbers. By 1779 the Southern Patriots have been suplanted by their French allies
as the major military force fighting the British and within a year have given up the military struggle leaving the French fight on alone in America.
The British are winning but in 1781 when peace is offered they refuse, in spite of not loseing the American colonies they have lost Minorca to the Spanish and it's strategic location make it's loss to much to contemplate. Peace comes in 1783 when the Spanish offer additional territory to the
British adjacent to Gibraltar makeing it more secure and the Spanish keep Minorca.
With the end of the War of the Borbon alliance the British refuse to accept direct American representation in the British Parliament and begin a process the sees the creation of the Dominion. The Slaves freed in the fighting move to Florida and create a Free Colony and slavery is only allowed in those places that already have it.
The Naploeonic wars occur and the war with Denmark starts with an invasion of Norway in 1802. This causes the Swedish to declare neutrality as they
had been prepareing their own invasion. In 1806 the British seize the French territory in America and a diplomatic insult from the French Nobility in exile causes the British to consider returning Lousiana to Napoleon and declareing their own neutrallity. They hold off this decision and stay in the war.
In 1814 the British launch an invasion of France through Brittany and with Russians, Prussians and Austrians in the east and Spanish in the south Napoleon isn't able to keep them all at bay and eventually surrenders.
The Peace being negotiated in Vienna in 1815 sees the British intent of keeping Brittany and Lousiana and the French monarchy threaten war but Napoleon returns from exile and the British threaten neutrality. Seeing that the French Borbons have no choice they agree to British demands and Napoleon is defeated. Hanover seeing it's fate over the last twenty five years decides to ask for an act of union with Britain to ensure that they are never swollowed up by another europen empire.
Without thinking about details I would say the Cecil Rhodes dream of a continous British territory reaching from Cape Town to Alexandria is
realised in the 1880s. The Opium wars against the Chinese are more successfull because of the additon of troops from the Philipines, not
British but Philipinos.
I can't think of credible reason for a British presence in Thailand or Indo China. The Arabian possessions stem from the 1890s but I can't be sure of if there will be a WWI or what form it will take. But overall I would date this map from about 1925.