At Westminster, an Early Day Motion is a motion tabled by an MP, calling for a debate on a particular topic. The motions rarely get debated, but they draw other MPs’ attention to particular issues. EDMs are a sort of petition system, exclusive to members of the House of Commons.
I had always taken it as a given that EDMs were a useful tool in a campaigner’s kit. If one Member of Parliament is allied to your cause, they can table an Early Day Motion… which then gives supporters of the campaign a reason to write to their own MPs about the issue. By requesting that your elected representative signs the EDM, you are effectively asking “please put it on record that you support this issue”. This is useful.
During the course of the Libel Reform Campaign, we made much of the fact that 249 Members of Parliament had signed EDM 423, which was a lot. It was also significant that the motion had cross party support.
The disappointing fact that some EDMs do not attract cross party support is often a useful data point. For example, of the 36 people who have signed EDM 37, condemning the imprisonment of Raïf Badawi in Saudi Arabia, none are from the Conservative Party, who are currently in government. Since Badawi is in prison for the crime of setting up blog that discussed liberalism, it is odd that no Tory wishes to put their name to it. Perhaps they simply haven’t been asked… but perhaps the Conservative whips have asked them not to, for reasons of diplomacy. (This is infuriating to campaigners, but as I blogged previously, there may be good and honest reasons why this is so.)
It is possible, however, that if one seeks genuine change rather than posturing, EDMs are a distraction. While working on the Raïf Badawi case, I wrote to some MPs asking them to sign the EDM. I received this reply from one Member of Parliament:

I very rarely sign EDMs for the following reasons. First, they have absolutely no impact at Westminster.
Second, PR companies and the like suggest to their clients that they should pressure MPs to sign them when they know full well that they are political placebos with negligible impact but they can claim that their influence has made MPs sign EDMs. 
Third, I am told they cost the taxpayer (each) about £300 a month and there are hundreds of them. I do not like that at all in view of my first two points.
One MP I could name signs almost every one, but I think that to be dreadful because he knows full well that they achieve nothing. But it gets that MP off the hook! Not one EDM has made it through to legislation in my time.

The EDM on libel reform disproves that last point, but the others are worth considering. The £300 figure is a factual claim which I will check. But if the EDM process is not particularly respected by MPs then it might not have the parliamentary influence that campaigners assume, and those ‘PR companies’ assert.