Thanks everyone for your advice.
The new computer (Dell Latitude X200) has a file transfer wizard; the instructions are very straightforward. Copy the relevant file and settings transfer program to a floppy, feed it to the old computer (Dell Latitude LT), connect the two together with a £20 serial file transfer cable and then watch the little dears merrily chatter away to eachother.
One snag - it took ages! I only wanted to transfer 350Mb of data from the folder I'd already prepared in 'My documents' - the transfer process took 16, yes, sixteen hours to complete!