What neutralises cat or dog urine stains on the carpet?

Lots of opinions and options listed here. I usually use vinegar and water, then flush with water.
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I use a spray from the vet called 'odour eliminator' made by Pet Care, and whatever's in it does exactly what it says on the bottle. It works just as well for human accidents as well before anyone wonders.

Thanks. I have read in a household hints guide that soda water does the trick.

Soda water will do the trick if the mishap is fresh, but once it has been there and dried a bit it isn't so good. On dry smelly patches dry bicarbonate of soda sprinkled liberally and rubbed in then vaccuumed up works well. You have to leave the bicaronate of soda on for awhile, overnight is good. Works well on milk smells as well, in fact a small saucer of bicarb is good in the fridge for fridgy smells.

I like methylated spirits (on the stain, not to drink!). It takes the pong out and evaporates quickly too.

Our vet surgery recommended surgical spirit (rubbing alcohol to Americans) when we took in a stray cat that kept having accidents. As well as neutralising bacteria, cats find the smell off putting so they don't return to the spot. Seems to work.