For the record, i have done 3 assessment centres and interviews for NATS, and i also know people in the HR dept. The reason they do not give feedback has nothing to do with 'national security' (possibly the bizzarest excuse ever) and 100% o do with the fact that they have hundreds of applicants and do not have time. (Cant be bothered). You can quite easily get feedback through data protection (people have used that excuse before) but all you will get is 'you did not meet requirements for (either/or) numerical reasoning, motivation etc etc... it will not be specific.
If you failed assessment centre then yuo really have only to think of the fact that you either didnt get enough questions right on one of the papers or you did not get the 'right' answers on the personality questionairs-although i have been told that if you dont pass that you are a complete nutcase (or lying).
most likely either the maths or the motivation paper (what they are most concerned about) which, for the motivation paper you need about 70% to pass.
dont worry about feedbak, the questions you got asked in assessment will be EXACTLY the same next time round (have been for years) so take the experience and learn.