I work in the recruitment industry following some 20 years in light blue and would echo much of the sage advice given.
The first hurdle for any applicant is getting your CV to 'register' with the recruitment agency/consultant. Recognising that there are likely to be a significant number of applicants for every position advertised it is an essential that your covering note/email identifies clearly some relevancy to the role - indeed that should be echoed in any opening statement on your CV.
Get someone else to critique your CV. Family/friends are fine but may not be as harsh as they should be. As already mentioned, the number of painfully obvious mistakes that are made in the presentation of CVs is frightening.
When applying for roles always try to make your CV bespoke - we have many generic skills; however, potential employers will normally expect to see a CV that demonstrates specific qualities. It sounds obvious but the detail should always be in any job description - if it is not then ring the recruiter/employer direct.
As a rule, we will always respond to applicants who have missed the mark with the presentation of their CV and I am happy to help out should you wish to PM me.
At present the employment market is reasonably bouyant and there is an appetitie amongst employers for engaging ex-military personnel. The very best of luck to those making a move in the near future.
Regards
Critter