Not sure that DVLA gives out out CCJ's buddy. Usually they give out Magistrate Court Fines which is not registered in the public domain the same as CCJ's. Plus CCJ's you have a month to pay them off afterwards which will strike them from your credit record.
That maybe completely crap but I think that is how they work.
CCJ's and defaulted loan payments are indeed a bar to entry until you have resolved them & can produce a letter of satisfaction from your creditors that indicate you have made good the debt. It's all to do with Security Clearance.
Magistrate Court fines for serious motoring offences (drink drive, no licence, no insurance, dangerous driving and suchlike) together with non-motoring civil offence fines carry a 5 year Rehabilitation period from date of conviction, subject to reduction by half if under 17 on date of conviction. Basically any fine that appears on the Police National Computer, paid or unpaid, carries a rehabilitation period (Speeding tickets & parking tickets are not recorded unless you receive a ban). You also have to provide documentary evidence of having paid the fine before you can enter service.