This usage is colloquially known as "blues and twos", which refers to the blue lights and the two-tone siren once commonplace (although most sirens now have a range of tones like Wail, Yelp, Phaser, and Hi-Lo).
From 1993-1998 a television documentary following Britain's emergency services was titled Blues and Twos for this reason.
Provision exists for a national standard to be required in order to utilise speed limit exemptions, but this has not been brought into force.
In the UK, vehicles used for certain purposes may have exemptions from some road traffic regulations whilst responding to an emergency.
Merely being authorised to use blue lights and sirens does not of itself grant exemptions from road traffic law.