It's possible, but it would almost be Russia's to lose rather than Britain's to gain. It would require the Russians to be pretty massively unsuccessful in their drives southeast from the Caspian, which is possible but not hugely likely. A British military conquest is possible, but some areas such as Afghanistan would be virtually impossible to hold, so it would probably have to be done by the pen in those areas. In this case, it would require Russia to be very aggressive, forcing some of the states into the British pocket, giving them the platform to then subdue some of the others militarily. Problem is, the Central Asian states were often so fiercely independent that they would go down fighting rather than seek aid off a foreign power. Perhaps if the Russians fail to invade a few times (while at the same time never throwing questions on their ability, as that would just be a morale booster for the khanates) and then try to make progress by a series of systematic massacre/genocides? Perhaps if the Cossacks get out of control?
I don't know. It's not an entirely likely situation, and would require some massive good luck for the British, and bad luck for the Russians.