They can be very slow and inefficient.
You will almost certainly need to chase them yourself to be sure (there are really probably only three big ones that most people use that you should focus on)
You should also check that the CCJ records of the Courts are properly updated too.
Most of the credit reference agencies allow you a 'free online trial' to check your own records (but then automatically start charging you a monthly fee if you don't cancel) - I am not sure this is fully legitimate as I believe they are actually obliged to let you see your own records for free - they just don't make that as easy as paying for a monthly subscription to do so. Do some research on this bit, and only take up the free trials once they tell you they have amended your records in order to check. (And don't forget to cancel before the free trial is up!)
It can be time consuming and a pain - but worth the effort.
oh edit - p.s. You should automatically get a copy of the Judgement if you were a party to the case. It should not cost any money.
Note: I am not legally qualified, just been around a few blocks. The sorry cynic.