The classic ancient answer (in Britain) was that to be a city a place must have a cathedral (don't ask me to define that!). Which means that somewhere as small as Ely in Cambridgeshire (population is about 15,000) by tradition gets to call itself a city.
A more formal modern answer, is that a large town might get to start calling itself a city if granted that status by the Monarch. There have been several competitions to designate towns as new cities. Preston, Stirling, Lisburn (northern Ireland) and Inverness have all managed to win the honour in recent years.
Outside the UK, the threshold to gain city status may be defined rather differently. In all cases we can take it that "city" status is relative to place and time. Cities are busy, densely and highly populated human settlements, with a (relatively) large variety of services and employment opportunities. But everything else about distinguishing a city from a town from a village from a super-city, is pretty much subjective.
A more formal modern answer, is that a large town might get to start calling itself a city if granted that status by the Monarch. There have been several competitions to designate towns as new cities. Preston, Stirling, Lisburn (northern Ireland) and Inverness have all managed to win the honour in recent years.
Outside the UK, the threshold to gain city status may be defined rather differently. In all cases we can take it that "city" status is relative to place and time. Cities are busy, densely and highly populated human settlements, with a (relatively) large variety of services and employment opportunities. But everything else about distinguishing a city from a town from a village from a super-city, is pretty much subjective.