If the aim at the Olympics is to win as many Golds as possible, not saying that should be the aim but it appears that is what Team GB is about, then you are best targeting funding at swimming, cycling and gymnastics. These sports offer multiple gold medal opportunities to the same person. If you are the best gymnasts you can win the overall team and individual gold and then pick up a few other golds in individual element finals. The velodrome also offers up great chances for the best rider. Swimming is the best of all though. If you are the best swimmer then you can win 8 golds on your own! When you see the same swimmer winning that many medals you have to wonder if the 50, 100 and 200 in a stroke really are different enough.
Sprinting does offer a good opportunity for multiple golds with 100, 200 and 4 x 100 but given how far ahead USA and Jamaica are it is hard to see how money (and er supplements) will help with that one!