Depends. Do you just want to record yourself the once? Or do you think it might turn into a regular thing.

In a sense, you do already have the bare minimum you need. Though that is the barest of bare minimums. I recorded some stuff directly into my laptop mic. It sounded OK - good enough to get me some gigs out of. When you say you want to record yourself singing, do you mean acapella? If so, then that simplifies things, and you could certainly get some half-decent recordings with your built-in mic and judicious EQing in Audacity.

But if you were going to be doing it regularly, I would say save up and buy:

1. a decent soundcard (in your case, something like an M-Audio firewire or similar)
2. a decent mic

These don't have to be hugely expensive and they also complement each other: a decent Firewire soundcard will have good preamps and phantom power for your decent mic.

Your soundcard will be circa £200, your mic circa £120 (most of the AKG condenser mics around this price point will do proud.

I'd also add to the shopping list two books:

1. Guerilla Home Recording (under a tenner on Amazon, bargain)
2. Mixing Audio by Roey Izhaki (for once you catch the bug)