The .303 Lee-Enfields are largely not used anymore. The rifle you must have seen is most probably the Ishapore 2A1 which is a locally-made version of the British SMLE (Short-Magazine Lee Enfield). This is chambered for the 7.62x51mm NATO round, otherwise known as the .308 Winchester i.e. the same ammo as the FAL/SLR or the HK G3.
It is old, sure, but make no mistake, it's a very good rifle with incredible stopping power. The only design-related drawbacks are it's length which makes it unwieldy in modern urban environments, and the bolt-action system. There are two ways one can go wrong with this gun. One is if it's not properly maintained, and two if the person shooting the weapon isn't properly trained.
For usual Police work, an Indian cop actually doesn't need anything more than a standard 9mm. And that's for Inspector-level officers...the Constables needn't even be armed. The prevalence of firearms in the hands of petty criminals is very rare. When armed police are required, cops in most big cities can now draw upon AKs (including the new OFB-made Ghaatak with P-rails which recently began being issued to Kerala Police). INSAS-1A (most probably Army stocks retired after taking on INSAS-1B & 1B1) as well as SLRs are also seen from time to time.
(Pic credit: Kunal Biswas)
It's likely the Ishapore rifle you saw is one of the batches that are well on their way out.
