Get yourself one of the bug screens (or even a small skima) from here:
http://www.pennineflyfishingguides.co.uk/torrentis.htm
If you can get in the water downstream of your rising fish and hold the screen in the water for a few minutes - you'll be able to see the size, colour and stage (emerger or full adult or nymph) of what is in the top few inches of water. Chances are there will be only a few different types of flies that are present in sufficient abundance to be worth imitating. This narrows down what is worth trying - but make sure you match the appropriate stage of what you are copying (you don't need to know the name of it though!).
In addition, look carefully at the rise forms - are they splashy? (possibly adult Olives or something similarly large) or small nebbing dimples? (possibly midges or other small items). Are they "head and tail" or "boil" type rises? (both of which could mean nymphs just prior to hatching or even emergers - of midges or olives or stoneflies).
At the very least look at what is flying around or in the bankside cobwebs or what you can see in the water surface (which is limited compared to what you will capture in the pale mesh of the bug skreen) and compare that to the rise forms. This should narrow down your choices to just two or three options.
Then its just a case of trying each imitation, making good/accurate presentations on an appropriately constructed leader (matching tippet length and diameter to size of fly, degreasing the last 12-18").
If you go through all your likely choices without success - have a very hard think about how to present your fly. Is there a better angle to cast from? Could you use a different cast to remove drag for slightly longer? Are you giving the fish too much "lead"......or too little.....
There's lots of things that will help you solve this problem, so you should have some fun in the process.