I read the article today, and I've read this thread with interest. It's got me thinking; I'm not lonely at the moment, although I certainly have been in the past, and a lot of my twenties were spent feeling desolately lonely.
I was thinking about why I don't feel lonely now, when in fact I easily could have recently, given my circumstances. We (DP and DD) moved from London to a small town two years ago. I don't have any close friends nearby, and didn't really expect to make any, I guess, having come from London where people don't connect that easily. For the first year, that was the case, and it didn't bother me, as we do have friends come to stay for the weekend every now and then, and I have a female friend or friends come and visit on a weekday for boozy (or not) lunches occasionally. A small group of mums in the playground were actually really friendly and always happy to chat, so that was really nice, but as has been said on here, there's a big leap between that, and actually meeting up and establishing a friendship. I know I appear to people to be very chatty and outgoing, but I'm actually a depressive (fairly well medicated) and a very anxious person. I'll chat to someone who chats to me, but then I tend to gabble and talk too much, and then afterwards I cringe thinking about how they probably never want to run into me again because I dominate the conversation and make crap self-deprecating quips all the time. The result is that social interaction with people I don't know actually makes me feel very anxious. I'm a very open person, and often feel like I say too much too soon. The upside though, is that the friends I do make, end up being close friends because they know that they can say anything to me, pretty much, and I won't be shocked.
So anywaaaaaaay..
I think there are two reasons I don't feel lonely; one, a few months after we moved here, we got a dog. Walking her, especially when she was a puppy, meant I met and got talking to loads of people. Obviously most of those are superficial interactions, but I had some really interesting conversations with such a wide variety of people. The notable thing about it was, that it's not all the Surrey yummy mummies I got chatting to - they're too busy jogging, or wearing their ipod, or walking with a friend, to notice that all the other people (often much older) are standing around chatting and laughing uproariously (I'm only 38, btw).
After a morning walk at a certain place that is particularly friendly, I feel like I've had my daily dose of casual, easy, relaxed chat. Also, I think having the dog shadowing my every move, every minute of the day, stops me feeling lonely. It's like DD, but without the incessant inane chatter. 
Two - a year ago, I started working very part time as a carer for an elderly local lady. She's lived here all her life so she tells me loads about the area when I take her out, and we have some really great chats (often quite surreal, as she does get a bit confused at times
). I feel like I can tell her most things (within reason, obviously, some of my wine fuelled chats with mates really wouldn't be for her ears...), and she was incredibly lonely before I started working with her.
So I guess my advice here is; get a dog, and befriend an elderly person. 
Seriously though, don't let your 'friend' sights rest only on other women in your agegroup and circumstances. I think friends can be found in the most unlikely places. Recently I hadn't walked at the dog-walking spot I mentioned for a while. On returning (after a month or so away), I was greeted by two late-middle-aged, rather camp (but actually straight) guys with their elderly shitzu, who were chatting to a guy I didn't know, and who shrieked
"THERE you are!! We were just saying, weren't we, how worried we've all been that we didn't see you and (my dog) for so long! We thought you'd been poisoned by one of those mushrooms you like picking, and we've been asking everyone if they'd seen you!"
And incidentally, I slowly slowly slowly got to know a few of the school mums, and then after one of them got a dog (see, it's the dog thing again) and we chatted more, she invited me to go along to a cooperative allotment some of them share. Since then, I can feel the 'friendly aquaintanceship' start deepening towards friendship. I think it takes time, which isn't easy when you're lonely!
I know this has become a total essay (see what I mean about gabbling on??), but just to agree with people who aren't from the UK being friendlier; when I lived in London and DD was little, I used to go to toddler groups, and eventually was befrieded by one lovely woman, who was British Greek, and introduced to her friends, none of whom were English! They were Russian, Hungarian, Indian and American, and incredibly friendly and welcoming - I think it's true that you have to make more of an effort when you are new somewhere.
I just wanted to say to all the lonely people; it does get better, and to widen your sights. Other mums aren't the only option for friends. How about volunteering with a charity or as company for an older person?