Hey Daveman,
Listen, I don't want to insult you with simple answers if you've already tried them, but I just wanted to save you some quid before you invest in more expensive solutions.
Make sure your cords are all good. Plug each directly between guitar and amp. If no problems, cords are fine.
I also assume that the output of your tuner does not make this noise going into other amps.
I believe that Rectifiers have effects loops. Try running your tuner in between the effects send and return. See what happens. Some guys will tell you not to use the effects loops of tube amps especially if the drive and recovery are internally operated by chips instead of tubes. They say if takes away from the purity of the tube sound. If you can't hear a difference don't worry. Some guys can hear grass grow. Note that you've introduced a solid state device in the chain via your tuner no matter where you put it.
These are just simple, quick things to start with. If the problem persists, e-mail me. There are still plenty of solutions before you invest any money at all. Fortunately you have a tube amp and that is my specialty. Let me know how you do.
Murf
Murf.