Nothing against the law per se, but your overtake could become another overtake that the Fire/ Ambulance vehicle may have to makeshould you be hampered further up the road by a junction or another hazard and you have just slowed them down unnecessarily.
Another thought is that the pilot of that vehicle knows where the fire / crash or other incident is - you don't & it may be half way through your overtake that you find out.
Can't remember anyone ever going past me on the way to a job but if they can do it ( legally though
) they're welcome to!