If you think it was that badly handled (and my personal feeling from what you've said is that it wasn't) then contact your local Councillor - you put them in power after all, so they are in competition with prospective replacements, and they want you to be happy constituents. If you feel that the services are that are that bad, then chances are your neighbours do too - so talk to them, and get them to forward their comments on too.
If you don't think that the issue is that serious, most Council websites have a handy page where you can complain either online, or give you a number to phone to speak to someone directly. You can report that you felt you were dealt with rudely (give as much info as you can) and it will be fed back. The form might even be
this one. No, Councils are not in direct competition with one another, but their performance is closely monitored and this sort of feedback is taken very seriously, especially if any of their services are outsourced.