Why do people always drag up Athenian 'democracy' in these articles? The government structures we associate with democracy are far more directly descended from Scandinavian and Germanic practices. The oldest still-functioning 'parliament' is the Althing of Iceland, which first met in 930 CE. For centuries Scandinavia and Germany made laws, passed judgements, resolved conflicts and elected Kings and chieftains through their system of regular things or moots.
The English Parliament (the 'Mother of Parliaments') was to all intents and purposes a combination of the Great Councils (witengamots) of nobles and clergy summoned by Saxon and Norman Kings and the Anglo-Saxon Folkmoots where local affairs were resolved by regular meetings of freemen in the shires and boroughs. When Simon de Montfort summoned two knights from each Shire and two burgesses to his parliament in 1264, it was likely that these representatives were chosen in moots. Over the centuries, then, the Great Council became the House of Lords and the moot-chosen knights and burgesses became the House of Commons. Nobody involved (except possibly some of the more learned clergy) knew or cared about Athenian democracy.
Ultimately, the body evolved into the UK Parliament we see today, partly due to the ideas of the Enlightenment, but mostly to the pressures and social changes brought about by capitalism and industrialisation. It is notable that no similar evolution has occurred in the United States Congress, which explains a good deal.