I've had a look in Disk Utility, and can't find a way to do this so I'm hoping someone will either know a way to do it, or know a tool which can do it for me.

Basically, I've got a drive which used to be split into two partitions. I no longer have any use for the first partition on the disk, and as such it is sat as empty space. I also had some empty space at the end of the drive.

Now Disk Utility gives me options to increase the size of the partition I want to keep (the "middle" one) but only allows me to extend it to the end of the disk.

What I really want to do is incorporate the empty space at the start and end of the disk into the volume.

Does anyone know how this can be done without formatting and wiping my data?

It can, but it's a potentially dodgy.
There's an app (not free, sadly) called iPartition that'll perform this piece of wizardry.

I'm not sure if there's any freeware offerings that'll do the same.
As usual, make a back up first.

Have you looked on the Apple support pages? I think that the answer is there.

I would find a spare external hard drive (USB 2 is OK for Intel Macs, Firewire if your Mac is an older PowerPC model) create similar partitions on it with Disk Utility, then use either Super Duper or Carbon Copy Cloner to clone each partition across to its equivalent partition on the external HD.

Boot from the external, format your internal drive with the required number of partitions and clone everything back again.

This would be far more reliable than any software method IMHO, which always carries a risk of data loss. If you do want to do it with software, I believe Drive Genius offers live re-partitioning, but it's not free software and at the price ($99 iThink) I'd just go with the cloning option myself. If you already have the external hard drive, it will cost you nowt - apart from your time!

The drive that I want to change the partitions on, is an external drive.

The problem is that I don't have another drive big enough to copy all the data onto in order to format it.

Buy one? Or better still borrow one from a mate. It's still gotta be cheaper than buying specialist software to edit the partitions, as hard drives as so cheap now.