I just finished my CPL having done the IR first and it worked out OK.
I did find the transition to the CPL phase hard though as I found it hard to resist the temptation to keep my head inside the cockpit for the first few hours of the CPL making it very difficult for myself. I also went over hours on the CPL - you can technically do it in 15 if you have an IR already but I didn't find it helped that much so ended up spending more money than I needed to.
What helped with the IR though was the fact that I was in current flying practice going into it and already held an IMC.
If I was doing it again I'd probably do the CPL first, but only as it would have saved me some money.
Hufty.