Britain occupied Corsica in 1790 but left in 1796. They could have feasibly just stayed (there was a significant pro-British faction on the island) and by 1814/1815 at the Congress of Vienna just pushed to keep the island. It'd be a super-malta, except the British would have Malta as well.
Meanwhile the British handed only finally returned Menorca to Spain in 1808 during the horse trading of the Napoleonic Wars.
Let's say Britain keeps both of these territories. The British military and economc presence in the Mediterranean is more sizable, resulting in the British butting heads with the North Africa Barbary States. TTL, Britain ends up grabbing Algeria rather than France.
Below is Britain's Mediterranean realm following the annexation of Algeria.
- Anglo-Corsican Kingdom
- Menorca
- Gibraltar
- Malta
- Kingdom of Algeria (the Dey is now the Baron of Algiers, with the British Monarch as King/Queen)
- United States of the Ionian Islands (Protectorate)
I imagine there'd be considerable migration to Algeria. Perhaps the British use it as a penal colony in place of Australia? Maltese, Majorcan, Corsican, Greek, and other immigration is likely. Indian, English, Welsh, Scottish, and Irish immigration will likely occur.
I wonder if the British could use Algeria as a relatively nearby release valve for the Irish when the famine occurs.
How would Algeria be different administratively? Would the situation for the average Algerian be better, worse, or about the same?