The origins of British democracy, at any rate, lie far from either Greece or Rome, but in Germany and Scandinavia.
Viking and Saxon invaders brought their tradtions of the 'Althing' and the 'Folkmoot' to Britain after the Romans left. The Saxon Kings who united England would hold, when needed, a 'witengamot', a meeting of jarls and senior clergy, but lesser thanes and cnihts would preside over moots to resolve local issues. The Magna Carta formalised the Great Councils which had replaced the witengamot under the Norman kings. When Simon de Montfort summoned the first real Parliament in the 13th Century, the 'Knights of the Shires' and 'Burgesses of the Boroughs' were elected by the moots.
Nowadays, the Great Council is the House of Lords and the Knights and Burgesses are the House of Commons. The moots remain in the form of Local Councils.