Meeting someone with no wingmen ;)

I recently finished up in a relationship. It wasnt a very long one, few months, but the break-up has been pretty hard on me so far. I know the best thing to do is dust myself off and get back out there. Heading out, socializing, activities whatever. Sitting staring at my laptop screen all day for the few hours I actually spend awake, thinking about the situation more is only making things worse.
Typically, heading out starts by rounding up the mates, right? However, all the people I know are in long-term relationships, so they are rarely free. I'm in my mid-late twenties ( :P ) now so I don't know if single's nights, speed-dating, things like that are really for me, I always imagined they were for a slightly older crowd, and I'd feel naff going them, I'm sure no one goes to them alone either! Feel naff for even considering them to be honest. I just don't know how to go about meeting someone solo, would much rather just meet someone 'naturally' than go the dating sites route.

I'm posting here on the off-chance that there is some option I haven't considered, or don't know about. Any advice would be appreciated.

All ideas (even the typical sarcy AH ones!) welcome!!