I've just watched all six episodes of the BBC historical drama "The Trial of Christine Keeler".
It was marvellous for the way it presented London life of the 1960s – the lovely old cars, the suave John Profumo with a gold cigarette case and lighter, elegant house parties at Cliveden, and the slightly dated idiom and slang.
Christine, at one point says "It's the rozzers…", which took me back in time.
Why "rozzers"?
Best Answer
GDoS suggest a possible origin from medieval French roussin:
Rozzer:
(also rawser, razzer, rosser, roz)
World Wide Words has other suggestions, none of which appears to be conclusive: