Hi -- The first recommendation is to stop applying for more credit, every time you apply that has a negative undesireable effect on the recovery of your credit file, instead concentrate on settling the second CCJ.
You have done really well so far by settling your liabilities in such a relatively short period of time, if you can get that second CCJ from the wholesaler marked as settled you will be well on the road to recovery, but your record still needs time for the seriousness of the CCJ's to be regarded of lesser importance when re-applying for future credit. The CCJ's stay on your credit record for a statutory Six year period unless you have valid grounds to apply to the court to have them "set aside," which it would appear that you don't have.
You could write to ex-creditors who defaulted you asking for their written permission to remove the old defaults, they need to provide a written agreement notice that you can forward copies onto the relevant credit reference agencies asking for the early removal of the old settled defaults. This action will substantially repair your credit file, then leave it for a further suggested period of 12 months after this before re-applying for a higher rate (easier to obtain) credit card that you always pay off in full every month. That will repair your credit history even further, also make sure you are registered on your local authorities electoral role, it all helps.
It's a catch 22 situation I'm afraid, you need a decent credit history to have a good chance of a successful application in the first place, but you also need a reasonable credit history to acquire that first foot in the door ....your other best friend in this situation is time.
The article below will also help explain in far greater detail, than I could reasonably post on here.