CATIII, generally if you've kept your credit card/bank statements going back the recommended number of years (as per HMRC guidelines), you should be able to find the purchases made through the travel agency, and that should be much easier for the travel agency to find your transactional details.
Once you have those dates, and you have received information back from the travel agency about your flight details, it shouldn't be a problem getting your details to the claims administrator and claiming back.
As pointed out by Globaliser, the PURCHASE date is the crucial one as you are charged air passenger duties and surcharges on THAT DATE.
Globaliser, the vital difference is that if the payment was made via credit card, the statements should continue to reflect that, and you can request old statements going back several years. If done online through BA.com or Virgin-Atlantic.com, the details will definitely be available. Through travel agents it's slightly more... how shall we say... challenging. If you are self-employed, or you run your own business, you will already be in the habit of storing your statements for the statutory periods. It'll be a case of going back into the boxes to find the details.
S.