I had success, yes, and the staff I spoke with were very supportive. They dealt with him so I didn't have to. From what they let on, he was very unpleasant on the phone but they gave him only two options: pay, or we'll deduct it from your wages. The staff took all that strain of the angry-rude-man from my shoulders.
I started by writing down as many details as I could: full name, date of birth, current address, national insurance number, place of employment / name of employer, and the date of the last time I had any money from him. I think I posted that to the CSA (which changed to the CMS). I think I looked up the postal address. (I hate phone calls. Weird, I know!) You can ring them if it's easier to start a claim.
Anyway CSA/CMS then rang and took details of the DC. It took weeks, not months, to establish his payment level. There were some arrears also, calculated from the day I made the claim. He ended up paying much more than I expected, and certainly much more than he would have done if he'd stuck to our voluntarily agreement. (He had had a tantrum about something or other, and I was sick of it.)
As your Ex works for the NHS, it should similarly straightforward. Having his national insurance number will really help.
Oh and by the way - they all threaten to pack in work and pay nothing, but the employed ones never do. It's hot air. If he harasses you over money, tell him you'll call the Police and do it if he persists.
Good luck.