What is direct democracy:
Direct democracy provides the people with the ability to contest the decisions of those they elect to administer the day to day governance of their nation, which representative democracy does not. It provides the people with control of all matters which affect their lives - be that at parish, county/city level, whilst also giving the people control at national level on matters affecting the future of their nation.
Why direct democracy:
Direct democracy provides the ability whereby a simple majority of those voting can be sufficient for decisions taken at parish/county/city/national level; but when the subject in question is to do with constitutional matters it is possible to require what is known as 'double majority'; this meaning that not only is the approval by a majority of the people voting necessary, but also a majority of counties/cities.
The benefits of direct democracy:
Switzerland is the modern pioneer of direct democracy and since 1848 the people of Switzerland have voted more than 600 times. More recently, between January 1995 and June 2005, the Swiss people voted 31 times, on 103 federal questions besides many more cantonal and municipal questions.
Let us look at the graphs in this article: people's initiatives (1893-2016); mandatory referendums (1848-2015); and optional referendums (1875-2016). Hover the keyboard mouse over each section of each bar and you will see the subject voted upon and whether the proposition was accepted or rejected, together with turnout and the percentage figure in respect of acceptance or rejection.
Compare the control the people of Switzerland have over their lives and governance of their nation, then contrast that with the people in the United Kingdom.