Just get a 24v laptop pwr supply and be done with it.
Ok - good advice. I ended up with a universal laptop psu from ebay that looked quite good - it has a 5v usb output too which should be useful.
I was expecting some sort of selector switch - but instead it has a system of various tips that attach to the laptop - each designed for a diff model of laptop, and each delivering a diff voltage.
the tips plug onto a little terminal block with 8 pins, so the voltage must be made up from a combination of pins. I tested every combination of pins with my meter and coould get a max of 16v, although I have verified that one of the tips when plugged in gets 20v. Is it adding up the voltages on the connector block?

I'm about to take my dremmel cutter to the 20v tip to see how it works, but thought I would pause and ask if anyone has a more scientific way of figuring it out...