From a Health & Safety perspective, you might need to tell your employers because if you are getting overtired and operate machinery of some kind in your main job, you could be more at risk through fatigue, of either having an accident yourself, or being a risk to other people. Also, there may be an issue of your second job representing a conflict of interest with your main employer, although if you work in a pub or do waitressing in the the evening, this may probably not be a threat if you work in an office during the day.
The main point is that you should not become so tired that you are unable to perform properly in your main job.
Where I worked previously, second jobs were allowed, but only provided your work performance on the "day job" was not impaired.. If your company has a Terms and Conditions of Employment handbook, this issue may well be covered there. If not, I would suggest that you are probably free to decide whether or not to reveal this. However, if your work colleagues know but your boss doesn't, this may give an impression of being deceitful by default. Either tell everybody, or nobody but be sure that your timekeeping doesn't slip as a result of having a second job.