The Daily Mail, unsurprisingly, has provided a misleading 'clickbait' title for the article. The title doesn't match up with what details they actually say in the article (and which you cited) - your quote doesn't claim Facebook is involved in a third of UK divorces, it claims it is involved in a third of last year divorces that cited unreasonable behavior as a factor. Possibly this claim also qualifies this is about divorces where the sourced law firm was directly involved, but that's not a clear implication.
According to this article at The Guardian, which cites as its source the Grant Thornton's 2011 matrimonial survey in the UK, unreasonable behavior was a reason in 17% of (then) recent UK divorces. Looking at the report itself, these percentages come from a survey question in which a lawyer would select three most common reasons for divorce.
This study seems to be from the same rough time-frame the Daily Mail article has been published, it is therefore very likely that a much more accurate title would be 6% of recent UK divorces citing Facebook as a factor.
I have looked into this more, results follow:
Noting that the linked Daily Mail article is dated Dec 2011 as of last edit, I've searched articles by DivorceOnline on their blog authored solely by the Divorce Online spokesperson, Mark Keenan. They have published an article in Feb 2012 saying
A recent poll indicates that a third of all English divorces in 2011 cited Facebook as a contributing factor, according to an article by Forbes.com. The 5,000 people polled listed a number of ways that Facebook activity played a part in their divorce. Reasons included sharing details of a spouse’s behavior, making negative remarks about a spouse and communicating inappropriately with someone of the opposite sex.
The article does not link to this poll. I have looked for it in Forbes.com archives, having found nothing (not claiming it doesn't exist, only having been unable to find it). Their next two articles, unrelated to the topic at hand, reference Daily Mail articles as sources and they do provide direct links to these articles.
Going back in the articles, the next mention of Facebook or social media and their part in divorces is the Sep 2010 blurb for an article on a different website, a long one, discussing social media and their influence in the context of family law and surrounding topics from many different angles. Under the heading Facebook and divorce, the article says:
There is now being coined the concept of a 'Facebook divorce' whereby one becomes reconnected to a distant, possibly adolescent, and therefore impossibly deeply felt affaire de coeur, idealistically perceived through the telescope of time, ultimately resulting in the present spouse being ditched.
The impact of Facebook on divorce has been well chronicled in the media (http://www.telegraph.co.uk/technology/facebook/6857918/Facebook-fuelling-divorce-research-claims.html) with claims that one in five petitions now contain reference to Facebook in some way.
20% is less than a third of all, but more than a 6% or even 17% of all! We may be on to something here, an older cited statistic perhaps? Continuing to the Dec 2009 Telegraph article, linked in the quote, we find this:
One law firm, which specialises in divorce, claimed almost one in five petitions they processed cited Facebook.
Mark Keenan, Managing Director of Divorce-Online said: "I had heard from my staff that there were a lot of people saying they had found out things about their partners on Facebook and I decided to see how prevalent it was I was really surprised to see 20 per cent of all the petitions containing references to Facebook. The most common reason seemed to be people having inappropriate sexual chats with people they were not supposed to."
Going back to the Divorce Online archives, I went all the way to the beginning of the blog in Mar 2009. No other articles even mentioned this research or any similar research. The first blog post does say that the author has had a personal blog before, but as he doesn't link to it, I'd assume it wasn't very rich on internal research publishing. There is an article containing results of their research in Jul 2009, Middle class adulterers are using Twitter to conduct illicit affairs. By Mark Keenan, however it is merely something to add to the "social networks", not the original Facebook claim.
Seeing the content type of the blog (sensationalist stories, poorly sourced; 'outraged' reports on the low quality and plethora of complaints about their competitors' services, contradictory articles) I'd say this is a circularly referenced claim, most likely made up. On a leaving note, here is an article from Jun 2010, Divorce-Online tweeted by Perez Hilton by Mark Keenan, in its entirety.
Divorce-Online have today been tweeted by none other than the King of Celebrity gossip Perez Hilton.
Perez refers the telegraph article that featured our research showing the word “facebook” appears in 1in 5 of all the petitions we deal with, sparking a debate on the evils of using social networking sites.
Now the big thing is that Perez has 2.5 million followers on his Twitter profile and his tweet about Divorce-Online was in the top ten re -tweets for today.
It just goes to prove that social media marketing does work!
Addendum: Other news articles citing the Telegraph Dec 2009 article seem to also mistake it for a US statistic, eg this one, copying the false attribution from here. This one simply attributed the statistic to the Feb 2012 article at Divorce Online, not to Forbes. Checking the references didn't seem to happen a lot concerning this particular tidbit, many reporting on it were comfortable with just repeating the claim on no factual basis.