Not sure where you are, but my experience was in Nothern Ireland. The environmental health came out at around 9.30pm (20 mins after I called them!) but they also stated that normally the noise has to be excessive after 11pm so yes they will definitely come out.
Is there no way you could have a word with them? Difficult I know but it could save a lot of disharomony. Failing that, just keep ringing the EH people, they are public servants after all and that is their job!
The police came out to these people several times (they were fighting in the courtyard, F-ing and blinding, you name it), but because it was an apartment complex the neighbours didn't know who had reported them. Not so easy to remain anonymous when you are in the house next door.
Good Luck
warpig