thats my take on it....
its not upto UKBA to enforce the law etc. They would leave it to relevant authorities.
As far as they are concerned, they will only check if you lied/withheld info in the app form. So, as long as you declare any "convictions" in the app form, caseworker can't refuse your app under the para which says the applicant withheld/lied about stuff on the application form.
Mind you, google official meaning of "conviction". Just because someone has asked you to pay outstanding amount is not same as "conviction". A law court must have issued some sort of sentencing etc. for it to be called a "conviction".
here is what i found on google.
"(criminal law) a final judgment of guilty in a criminal case and the punishment that is imposed"
http://www.audioenglish.net/dictionary/conviction.htm
You will need to find if non-payment falls under "criminal law" or "civil law". if its a civil law, then i dont think you are convicted, so to speak.
I should point, im not a lawyer, and thats just my opinion which makes sense, to me atleast
regards