As you are in the UK, one possibility might be to borrow them through the British Air Mail Society's lending library. They are a non-profit club of people interested in airmail philately. If you are a member of the BAMS you can borrow books from their library through the post. Here is a link to their website:
http://www.britishairmailsociety.co.uk/ I know they have books from the 5th and 6th editions of the American Air Mail Catalog, but I am not sure if they have any of the first 3 volumes of the new 7th edition. If not, you can buy them from the American Philatelic Society which is the main US non-profit organization for philately. I do not know the shipping cost to the UK, but at book post rates hopefully it would not be too steep. Another possibility might be to buy a used set of volumes of the fifth or sixth edition of the AAMC on
ebay, or you might get lucky and find one or two volumes of the 7th edition. The 7th edition is still in the process of releasing a few more volumes in the coming years. Keep in mind that these are labors of love by volumteer experts and so they are not on a very predictable schedule and they do take a long time to get issued. Another thought if you are interested in airmail covers and first flights, especially US ones but also ones from all over the world might be to consider joining the American Air Mail Society which is the main non-profit club for airmail philatelists with a main, but not exclusive, interest in covers to and from the US and domestically within the US. This society is in the process of expanding its internet presence and making it easier for people from other countries to join at the same rate as US members by offering very soon its monthly journal electronically to avoid mailing costs. You can look into the AAMS at
http://www.americanairmailsociety.org/ Currently members from the UK would be charged $60 for a membership but as I mentioned that is likely to change very soon to $30 which is the rate for members in the US. You can contact them and ask them about the details. They are also building a new Facebook page for people to ask questions and share expertise on air mail covers electronically. They are the ones who write and publish the American Air Mail Catalogs so they are the ones with the serious expertise and they welcome new members at all levels from complete beginners to seasoned expersts.