This paper proposes a framework to model market-driven operational scenarios of distribution systems that comprise multiple stakeholders and flexibility products. The framework exploits an iterative algorithm and optimization procedures to perform flexibility demand-supply modelling, market clearing, ancillary service tendering, and network modelling in a coordinated manner. The proposed framework has been applied to a realistic case study that comprises a real distribution network in England, official forecast data for flexible demand (i.e., heat pumps, electric vehicles, industrial and commercial demand-side response) and distributed generation (i.e., photovoltaics, wind and storage). To envisage competition at the whole system level, the market prices for the main electricity system services (i.e., frequency response and operating reserve) have been informed from a whole energy system modelling. The numerical study showed that market-driven distribution systems can facilitate cost-effective operation of the whole electricity system, delivering value to all main stakeholders, including network customers, suppliers, distributed generators, aggregators, distribution and electricity system operators. However, a comprehensive modelling of a complex ecosystem offered in the present paper, is necessary to find the efficient configuration of a distribution system, including a set of flexibility products, rules, price signals (i.e., tariffs and charges), and coordination between stakeholders.