Last night I gave up on strangling the taps in the shower to stop their insidious dripping and accepted that it was time to try the washers I'd bought. These are a new type with a recess in them to use the water pressure to buttress against itself. They're made by Doust Plumbing Products, a firm operating out of my home town, Perth, Western Australia.
Here's a link to the page on their site which explains how they work.
I found they worked pretty well but I'm having to turn the taps off harder than I expected. I'm wondering whether it's that the tap needs reseating or the newfangled washer is not up to the contents of the blurb. Time will tell.