Sounds like as you pedal the tension is skewing the rear wheel, so it can't be tight enough.
Have you taken a close look at the QR as you tighten it. It could clamping against the end of the axle but not tightening against the drop out properly. If so it could be your axle is to long.
Thanks R, that did actually just occur to me. I was planning to repack the wheel, so I'll check that I have even amounts of axle sticking out beyond each locknut and that it's not wider than the dropout.
On a similar note, I thought I'd resolved the problem in my last round of fettling. I'd mounted the conical spring on the QR skewer on the wrong side so it was sandwiched between the dropout and the QR nut. Putting on the correct side (where the QR nut has a recess to take it) means the nuts are both flush against the outside of the dropout, but it still slips!
I guess mounting a wheel in horizontal dropouts is just something that I never saw my Dad (or anyone else) do, so I've just not worked out the "knack" for doing it. Is there a particular trick?