The gov.uk petition site is one of the most popular and regularly gets a "pulse of the nation" issue brought to parliamentary and media attention. (I suppose that is in many ways the prOblem we just faced)
For example Turing was given a pardon after JGCumming of HN fame started a petition on there.
It's not perfect, it is "just" a voting site, but we have had a taste of direct democracy - we might just start to like it.