The GP/nurse/Dr would usually say if it has to be the first pee of the day. If they said nothing it generally means anytime. Mid stream wee is only on certain cases (pregnancy/gyny probs are just two examples of this) but not always the case though!!
If it was necessary to fast for 12hrs before the sample is taken, then you would have been told as such. Taking blood to check for cholesterol levels requires this strict practice. i.e if the blood is taken at 9.00 am then you must not drink or eat (anything) after 9.00 pm the previous evening. As I said before you would have been told if this was the case.
Having said that :
Err on the side of caution - and use the first pee of the day as it is more concentrated, and will give a better indication of any problems (or not).