It's a very interesting question- and one perhaps those of us who have lived in different countries, with different types of democracy, maybe asking ourselves more often than those who have always lived in the same system (mind you that applies to the education system, health care, etc too).
The First Past the Post system is certainly cited as a system which really is not very democratic, for the reasons you stated. Especially when the second Chamber is not elected, and has groups automatically represented that do not reflect the current UK situation (as in one religious group only- but at least inherited peerages have gone).
I currently live in a democracy where everyone can bring about a project for a new law or project- as long as they can gather a certain number of signatories. If they do, it has to be voted on by the people- that can happen at local or national level. It's very very hard work to study all the issues to be voted on- perhaps 5 -6 times a year, often 4 or 5 totally different issues.
It sounds ideal? But is it? We have seen how manipulated people can be by the Press, especially some sectors of it- and how lies in campaigns go unchallenged. The right wing party in Switzerland, called UDC in the French part and SVP in the German part- are notorious for putting full magazines of shameful posters, cartoons and lies in every letter box before any such vote- like UKIP they are supported financially by some very rich people and have vast amounts of monies for their campaigns.