If anything I would say the recent spate of incidence have DECREASED siren use, insofaras, drivers are less likely to drive fast and especially drive through red lights when siren are at their most useful.
I know some areas now have the twos and blues monitord externally, to avoid abuse of them and many emergency vehicles now have "black boxes" which will record their activity.
If they use them at late at night, particularly the old bill, may I suggest you simply write to the Inspector of that station and request they (no pun intended) tone it done a bit.
However, I take your point that the sirens will give advanced warning to criminals, but take this obvious example.
If you or a loved one were getting attacked, raped, followed or in immediate personal danger, would you not prefer the villan to get scared and run off before he or she hurts you further?
I assume you are referring to burglars on premises. If this is the case, most decent alarm companies will have a silent detonation for this very purpose. When reported to the police, say via ADT, or direct, this will be flagged up for the officer attending to make a silent approach. They even use terms for such approaches.
Therefore, unless the Bobby is a complete kn0b, which many are, rest assured when the sirens are on he or she is not going to a "burglars on"