Would a change in the voting system improve democracy in the UK?

Currently, the UK uses the First Past the Post (FPTP) voting system to elect the representative parties in the general elections, however people have questioned whether it is democratic or not.

This question has been practised in 2011, when a referendum was held to change the voting system to the Alternative Vote. The Alternative Vote is a preferential system, where the voter ranks the candidates in order of preference. For example, they put a number 1 next to their first choice etc, rather than putting an X next to one political party. British citizens showed that they did not want the voting system to be changed to the Alternative Vote because 67.9% voted No and, less than half voted Yes at 32.1%.

A change in the voting system would improve the UK's democracy, because it produces a fairer result and electors can vote for their first choice and last choice candidate without fear of wasting their vote.  Also candidates are elected outright if they gain more than half the votes as first preferences. If not, the candidate that loses is eliminated. As a result, the political party that is not the most popular by the people, it will be eliminated.

However, the Alternative Vote may not improve the UK's democracy because the vote is not changed as the electorate votes for their preferred choice, which is almost exactly the same as the FPTP system. Also, the Alternative Vote does not give the electorate a more direct say in politics, as they are voting for the representative parties to represent their constituencies; their preferred and least choice is recognised, not their personal view which is shown through direct democracy and referendums. Also, this voting system can produce a more disproportionate result than FPTP and the least favoured party may be unpopular because of the influence of the media and different opinions.

The Alternative Vote is currently used in Britain to elect the leaders of the Labour Party and the Liberal Democrats which has proved a success. However, if the Alternative Vote is a better voting system than FPTP, why aren't we using it for the general elections?