The Government scheme for e-petitions (http://epetitions.direct.gov.uk/) which the public can initiate and/or vote on is now live. If a petition can garner 100,000 votes in a maximum of a year, Parliament will then consider whether to debate the subject of the petition. Although there is no guarantee of a debate, it would be politically difficult to refuse one because a failure to debate an issue would nakedly reveal the scheme as simply a piece of political elite PR.
There are already quite a few petitions, the large majority being serious. The most popular subjects are those which the British political class wish they could censor out of public debate: immigration, race, foreign aid, Islam, the EU, the corruption of the political class, warmongering, weakness in punishing criminals, the death penalty, the harassment of motorists, the cost of transport and the imbalance of the devolution settlement with England left high and dry without a political class to look after her interests.
There is a good deal of duplication, not least because the search function is poor and it is difficult to see exactly what has been put up by other people. Nonetheless, it gives a good idea of what the public is most interested in.
Below are links to the petitions with an English interest which have already been sanctioned as of today. Where there are misspellings or typos, this is because those moderating the submissions are putting them up on the site without correction.