Hello rainmaker, i think the best start would be taking the course to be AAT and ACCA certified here.....
You have to invest in yourself first before you get the return of your investment which is a good accounting job and accounting career here in the uk....
I think once you have the AAT and ACCA qualification, it will be easy for you to get an accounting job regardless of your lack of accounting work experience here....
As you just mentioned, you are working here and i suppose you've been working for quite a while having been here for 5 years already....
Although you're working in a different field, what's important is you already established a working history in the uk and got references/referees to vouch for that....
And don't fret about not getting hired after the AAT/ACCA course for lack of accounting work experience, chances are, it's more likely the opposite...
Be positive and work your way up to the goal you set coupled with diligence and hardwork - it will surely pay off