Well, at long last, it seems that I have a Stevenson screen set up such that there is, at worst, only a small anomaly relative to the sort of readings one would expect from standard Met Office stations (by small, I mean quite possibly no greater than a degree Celsius on the sunniest days, which is pretty good for a back garden site)
I have had an automatic weather station since 22 June 2005, but until November 2006 the temperature sensor was placed on the side of a hut, giving anomalously high readings by both day and night in summer (due to heat radiating off the hut) and anomalously low overnight readings in winter (due to exposure).
November 2006: set up Stevenson screen but with only one set of louvres; result; anomalously high readings in sunshine. Put on the second set of louvres and it worked fine until February/March when I started getting anomalously high readings again.
The instrument was situated right next to a fence; some members of this forum suggested that the proximity to the fence, when heated by the sun, was probably a factor. I have recently had it moved further away from the fence, and it seems to have worked. So for the moment at least, it looks like I'm not going to have to keep 'calibrating' my readings relative to what my two older, more primitive thermometers are showing for days when the Stevenson screen readings is anomalously high.
The last few days, incidentally, have been a big test of this, with plenty sunshine every day except Friday. My maxes were 18.8C on Thursday, 12.3C on Friday, 16.1C Saturday and 16.3C Sunday; pretty promising readings I'd say.