I'm not sure what LMA entails & if you have any experience on combat cas but I'm 100% sure that if you can get some time volunteering in a A+E environment ect you should be beneficial to a team some where.
The work is hard to get into, there is work out there but once your in don't expect the pop star wages.
What certification/CP courses have you got/done? From that members here with better knowledge can assist you but! in any case..
Don't settle on a billy basic CP course, every man leaving the Army/Navy/RAF will have enough learning credits to attend a billy basic course and entering at that standard is futile, try and head for the 'Higher tier' courses, obviously always make sure you're getting your moneys worth and that it's a financial and socially suitable for you (Debt/Wife/Kids ect)
If a UK course is £2,000 and gives you 3/4 quals see if you cant save up. Should another course cost £3,500/4,000+ but gives you a whole bunch more certification and experience go for that (cant stress Experience enough)
On a side note/Story, a good friend of mine working in Africa had a few new team members turn up, one guy had Medical qualifications coming out of his ears (he was a civvie with a low level of combat trauma experience)! his mum n' dad paid for what he needed and he was employed solely on his paper (Which he may have 'elaborated on'). long story short a few days later some stuff happened and his expertise were called on and he faltered at the final step and cost one of the locals their life by being hesitant.
Network, get on Facebook pages and Linked in, subscribe to paladin jobs, don't 'Cold Letter/C.V' companies a phone call goes further, head to some seminars, meet 'n greet some people, call on old friends who may be in the business.
Don't confine yourself to 'Hazardous' work, its brimmers with guys who've just left the mil' wanting to look cool instead of working hard. Don't confine your self to Iraq and AFGH again it's saturated, do some re-search and look at different countries. think outside the box i.e is it always people who need protecting??
Be realistic and don't expect huge pay or work right away especially if your not niche, i.e Medic, TL, Driver, Language ect
Have a back up for periods of unemployment i.e If you qualify in 'HECPO' and there's no positions for 9 months have some work to fall back on and again get on some courses and get experience.
Bu that's about it,... that's my thoughts on it, people may say it's rubbish ect but I find it all to be quite subjective.
EDIT: Many job adverts will say '1 year PSD/HECPO experience required' this is generally not required and will be over looked should your military service be front line/hostile.
Having spent most of my adult life in the shit tips of the world I now prefer my air conditioned office with the odd trip to the field.