I'm doubting the likelihood of the British switching sides. Muhammad Ali Pasha was a major figure in fighting the Greek Rebellion in the 1820s, which put him at odds with the British, and any way you slice it, a divided Ottoman Empire is far less likely to be an effective bulwark against Russia.
One idea I do find very interesting is having this play into the Great Game - in the 1830s Russophobia in Britain was just starting to take root, and the fear that a Russian army could march from Constantinople to British India was real (for some reason). A forced brokerage of the Convention in which Muhammad Ali Pasha gets his independent state could lead to, a few years down the road, Russian intervention in the rump Ottoman Empire over persecuting Christians or some other convenient casus belli. Set up a Russian puppet state astride the Sea of Marmara (I'm imagining a ruling class of Russian immigrants mixed with Pontic and Asian Greeks), and suddenly the whole situation becomes very frightening to the British, who would likely draw Greece closer into their fold.
But back to Muhammad Ali Pasha, expansion is limited to a specific window. Once it becomes clear that the Ottoman Empire is up for division among European powers, it's a race against time for Pasha. The Maghreb would be a natural expansion, but I'm not sure he could beat the French there, and the same goes for the Russians in Anatolia and the British-backed Persians in Iraq. He could certainly gain some traction in any of these locations, but all would be contested.
In reality, I think Muhammad Ali Pasha would be more likely to follow a European-style nation-state model for his Egypt. He was typically very European-minded (his armies were successful against the Porte's due to his relentless German-inspired drilling techniques), and his empire would primarily be composed of what we think of as the "Arab World" (minus the Maghreb and parts of Arabia). Attempting to forge a singular Arab-Egyptian identity for his new nation state (with colonies in Crete and Sudan) would be the model I'd likely think to see Muhammad Ali Pasha take, as opposed to attempting to conquer and hold the whole of the Ottoman Empire and get recognized as Caliph.