Best way to show relevant experience when applying for a loosely related Masters? I am currently in full time employment, but looking to return to University in order to complete a Masters in Computer Science in 2018, so I have plenty of time to implement your suggestions here.

My Bachelors was in an Economics related field, but I only managed to achieve a Third, due to personal reasons and a general lack of passion for the subject area, I should have done a Bachelors in Computer Science, but hindsight is 20:20

I graduated around three years ago and have been in positions with a heavy programming element, having implemented some projects using OOP and T-SQL on a regular basis in real life applications. I believe I will be able to handle any of the programming requirements of any such Masters in the Computer Science field because of this.

Obviously, institutions requiring a strict degree level are closed to me, but many institutions I am interested in state that work experience will be taken into consideration.

How do I best present my experience and attitude to these institutions?

Edit: Thanks for all the good advice so far, just to add that I am UK based, but you have given truly actionable steps so far.
All the usual advice about writing effective CVs and cover letters applies here. Additional advice:


Emphasize the positive and don't explain any negatives, since I really don't see any negatives in your story.
I suggest you take a couple of computer science courses before you apply, in order to (a) get your feet wet, (b) demonstrate your ability to be successful in a graduate CS program, and (c) garner at least one LOR in the target field. You can audit if money is an issue. 


I recommend taking one course per semester if you are working full time. Choose a challenging but doable course that you're truly interested in.