Axis & Allies - Opening strategies for the U.K.
I think there are three basic strategies for the UK:


Focus on India - with this approach, the UK cedes Africa to Germany. On the first turn, the UK builds a factory in India and uses its transport to move its two troops in Egypt to India, as well as the Egyptian tank and Syrian infantry into Persia (to move into India next turn). The fighters that start in the UK are moved to Karelia and then to India. For this tactic to work, UK must build troops and tanks in India each turn and continually harass Japan in Burma.
Focus on Africa - here, UK cedes India to Japan and focuses on holding Africa. UK starts by moving her troops and fighter from India into Egypt. Sometimes people will build a factory in South Africa when going with this approach.
Ignore Africa and India in the Early Game - with this approach UK does not build any factories. Some players build a bomber the first turn to have two bombers to take out the German fleet in the Mediterranean. Others build nothing the first turn, saving it for a carrier and transports for turn two. The general strategy here is to bide your time, prepare for a joint invasion of Africa and/or France with the US, and then make your move. In this approach, Germany will usually take Africa early on (although they won't hold it presuming their navy has been sunk) and Japan will take India early (and will hold all of Asia for most of the game).


The Focus on India approach is designed to slow Japan down, to make her focus on building up forces and taking India rather than moving west toward Moscow. Against weaker players you may be able to force Japan off Asia from this factory (with reinforcement fighters from UK via Karelia), but against stronger players the factory is doomed.

The Focus on Africa approach is aimed at bottling Germany up in Europe. This works best if you still have your Med sub after turn one and if you were fortunate enough to take out a number of German fighters when they attacked the UK sea zone. With this approach you need to kill off the German Med navy ASAP and then reclaim Africa from within. This almost always works against weaker players, and usually works if Germany has poor rolls at the beginning. If Germany had decent rolls and the player is good, you're going to lose your South African factory sooner than later.

Personally, I prefer and usually play the Ignore Africa and India in the Early Game, especially if I'm going against someone who is a strong player. With this approach you don't spend any additional money or time on India or Africa in the early game. Instead, you build transports, a carrier, and coordinate with the US to take Africa back later (after the German Med navy is destroyed) via landing at Algeria from Spain Sea Zone. With this tactic you are letting Japan have Asia without much effort, so you'll need to make sure Russia heavily fortifies her capital and ensure that the US/UK can get their troop pipeline into Karelia going sooner than later.

If you haven't yet read Don's Axis and Allies Strategic Essays, I heartily recommend them. They give a good overview of the Axis and Allies primary goals and tactics, and then delve into suggested opening moves and game-long plans for each power. (Don is a proponent of the Focus on India strategy for the UK.)