It is now possible again to set up a petition for a subject to be debated in Parliament. When a petition reaches more than 100,000 signatures it must be debated in Parliament.

You can sign a current petition or start a new one at:
https://petition.parliament.uk/

Current petitions include:

A vote of no confidence in the Health Secretary Jeremy Hunt:
https://petition.parliament.uk/petitions/104334

Imposing taxes on foreign investors buying property worth more than £3.5 million:
https://petition.parliament.uk/petitions/104311

To sign you must give a valid email address (which is not published) and respond to a link which will be sent to that email address.