I think the whole point of the government petition website is to gauge public opinion. I think it'll do more than 'nothing'. I'd agree though, write letters as well.

It actually does less than nothing.

Since an e-petition site like the one linked gives people opposed to an issue the impression that they've accomplished something, those people are that much less likely to do something substantive to resolve the issue they're concerned about [Citation_Needed -- I couldn't be bothered to find it].

So, less is actually done to oppose the issue than if the site never existed in the first place. It actually helps those who are in favour of the issue opposed.

E-petitions aren't useless: They're worse than useless.

This might be what you're looking for - http://www.snopes.com/inboxer/petition/internet.asp

Snopes.com on whether Internet Petitions serve any real purpose.

How about all the times the e-petitions on number10.gov.org have been reported in the mainstream media?

Now each article which reports on the issue will be able to say "An issue which has seen X sign a petition against it".

Also it's likely to make the news in more places.

But how many of those e-petitions with the media traction actually got meaningful results, other than making the news in more places?