Your best bet would be to get on a good graduate scheme if you want to go straight into industry, which means forgetting about mailing out CVs, but instead going for applications through websites. Although not currently run, BA for example used to have an enviable graduate scheme, however produced too many managers as a result. Schemes such as that are best for that career, however to get into those you might perhaps consider joining the Royal Aeronautical Society in order to make contacts within the industry.
As an alternative, joining a professional services or consulting firm is also not a bad move, since you will gain the top to bottom knowledge of the companies within the industry that are hard to obtain simply by working at one level within a company itself. McKinsey or Bain management consulting have practices in those areas - see:
http://www.bain.com/bainweb/publicat...s_overview.asp
or look on the McKinsey website at the McKinsey quartely, which contains aviation and transport articles.
Additionally chartered accountants also have many skills that the airline or airport companies are interested in poaching in order to financially analyse the company strategy, again with much of a broad awareness of the whole company rather than individual areas.
Other aspects along which you might want to develop your career in order to get into that field might be the MSc in Aviation Managment (I forget the exact field) that is run at Cranfield, which is highly-regarded and from which graduates are head-hunted into strategic positions within companies. MBAs would also be useful.
The problem you may have is that you want to work in that company, but you give no indication of the field in which you are interested. An awareness of the industry is fantastic, but are you aware of the many roles that are available, and what do you want to get out of it in terms of a career path?
Do you want a financial career, general management, or strategic of some sort? HR? Head office? You need to narrow that down before you apply, since no one will reply where you are not applying for specific posts in many circumstances.
Hope this helps.