The content of the petitions listed here is the copyright of someone, but it’s not entirely clear who it belongs to. The general terms and conditions on the Prime Minister’s website state that all content of the site is Crown Copyright except where otherwise noted, but the terms and conditions of the E-Petitions section don’t say anything about assigning copyright of your petition to the Crown. You can’t assign copyright by default - you have to explicitly agree to it in the terms of any system whereby you submit it to a third party - so the logical assumption is that copyright in the text of each petition still belongs to the original author. The PM’s office does own the database right inherent in the E-Petitions site, but the amount of content re-used here is so small compared to the entire E-Petitions database that the probability of it being a significant extract is remote.
The question, therefore, is whether the re-use of petitions on this (or any other) website is “fair dealing” under UK copyright law, or whether the petition creators have the right to prevent this site using their content. It seems most likely that the clause in UK law permitting re-use of copyright material for the purposes of “review or comment” applies here, since the whole point of this site is to allow people to comment on petitions. However, in order to avoid any unnecessary conflict, any petition will be removed if the original author asks for it to be removed. In order to minimise any privacy issues, the petitions presented here do not include the name of the original author - the point is to allow people to comment on the petitions themselves, not the people who created them.
If you are the author of any petition included on this site and you want it to be removed, then email ‘one {at} triffle.org’ (making the obvious substitution to make that a valid email address) saying which petition you want removed and giving enough information to show that you were, in fact the original author.