Unsurprisingly, my earlier bodge was less than ideal and the handlebar had a tendency to loosen over time. I found an extremely satisfying solution however that should be known to all owners of bikes with 21.1mm steerers. It's this 20.8 to 28.6mm quill adapter from Muqzi on eBay, designed for kids' bikes. The 20.8mm diameter is close enough to 21.1mm (especially with the expanding quill) that it fits the Raleigh steerer just fine.
So out came the crowbar, prised off the old single-bolt steel stem and stuck a modern one on. No more loose handlebar.