I have come across a service shaft in a block of flats, it has fire doors on each of the three levels but no fire stopping between each floor, so the shaft is open through each level. should each floor be fire stopped or is it acceptable for the open shaft. I would have thought a chimney effect would spread the smoke and heat through each level

It's a protected shaft, complies with Building Regulations and other fire safety guidance. It's an urban myth that these need stopping routinely and sadly many building owners have wasted money on doing this either on the advice of those who don't know what they are doing or are fleecing the owner as they also do the works.